BuyFind*arrow_forward*

7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 4.4, Problem 55E

Textbook Problem

1 views

**Combining Logarithmic Expressions** Use the Laws of Logarithms to combine the expression.

**55.** ln(*a* + *b*) + ln(*a* − *b*) − 2 ln *c*

To determine

**To find:** The combined expression of

Use the laws of logarithms and simplify the expression as follows.

Precalculus: Mathematics for Calculus (Standalone Book)

Show all chapter solutions

Ch. 4.1 - The function f(x) = 5x is an exponential function...Ch. 4.1 - Match the exponential function with one of the...Ch. 4.1 - (a) To obtain the graph of g(x) = 2x 1, we start...Ch. 4.1 - In the formula A(t)=P(1+rn)nt for compound...Ch. 4.1 - The exponential function f(x)=(12)x has the...Ch. 4.1 - The exponential function f(x)=(12)x+3 has the...Ch. 4.1 - Evaluating Exponential Functions Use a calculator...Ch. 4.1 - Evaluating Exponential Functions Use a calculator...Ch. 4.1 - Evaluating Exponential Functions Use a calculator...Ch. 4.1 - Evaluating Exponential Functions Use a calculator...

Ch. 4.1 - Graphing Exponential Functions Sketch the graph of...Ch. 4.1 - Graphing Exponential Functions Sketch the graph of...Ch. 4.1 - Graphing Exponential Functions Sketch the graph of...Ch. 4.1 - Graphing Exponential Functions Sketch the graph of...Ch. 4.1 - Graphing Exponential Functions Sketch the graph of...Ch. 4.1 - Graphing Exponential Functions Sketch the graph of...Ch. 4.1 - Graphing Exponential Functions Graph both...Ch. 4.1 - Graphing Exponential Functions Graph both...Ch. 4.1 - Graphing Exponential Functions Graph both...Ch. 4.1 - Graphing Exponential Functions Graph both...Ch. 4.1 - Exponential Functions from a Graph Find the...Ch. 4.1 - Exponential Functions from a Graph Find the...Ch. 4.1 - Exponential Functions from a Graph Find the...Ch. 4.1 - Exponential Functions from a Graph Find the...Ch. 4.1 - Exponential Functions from a Graph Match the...Ch. 4.1 - Exponential Functions from a Graph Match the...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Comparing Exponential Functions In these exercises...Ch. 4.1 - Comparing Exponential Functions In these exercises...Ch. 4.1 - Comparing Exponential and Power Functions Compare...Ch. 4.1 - Comparing Exponential and Power Functions Compare...Ch. 4.1 - Comparing Exponential and Power Functions In these...Ch. 4.1 - Comparing Exponential and Power Functions In these...Ch. 4.1 - Families of Functions Draw graphs of the given...Ch. 4.1 - Families of Functions Draw graphs of the given...Ch. 4.1 - Getting Information from a Graph Find, rounded to...Ch. 4.1 - Getting Information from a Graph Find, rounded to...Ch. 4.1 - Difference Quotients These exercises involve a...Ch. 4.1 - Difference Quotients These exercises involve a...Ch. 4.1 - Bacteria Growth A bacteria culture contains 1500...Ch. 4.1 - Mouse Population A certain breed of mouse was...Ch. 4.1 - Compound Interest An investment of 5000 is...Ch. 4.1 - Compound Interest An investment of 5000 is...Ch. 4.1 - Compound Interest If 10,000 is invested at an...Ch. 4.1 - Compound Interest If 2500 is invested at an...Ch. 4.1 - Compound Interest If 500 is invested at an...Ch. 4.1 - Compound Interest If 4000 is borrowed at a rate of...Ch. 4.1 - Present Value The present value of a sum of money...Ch. 4.1 - Present Value The present value of a sum of money...Ch. 4.1 - Annual Percentage Yield Find the annual percentage...Ch. 4.1 - Annual Percentage Yield Find the annual percentage...Ch. 4.1 - DISCUSS DISCOVER: Growth of an Exponential...Ch. 4.1 - DISCUSS DISCOVER: The Height of the Graph of an...Ch. 4.2 - The function f(x) = ex is called the __________...Ch. 4.2 - In the formula A(t) = Pert for continuously...Ch. 4.2 - Evaluating Exponential Functions Use a calculator...Ch. 4.2 - Evaluating Exponential Functions Use a calculator...Ch. 4.2 - Graphing Exponential Functions Complete the table...Ch. 4.2 - Graphing Exponential Functions Complete the table...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Hyperbolic Cosine Function The hyperbolic cosine...Ch. 4.2 - Hyperbolic Sine Function The hyperbolic sine...Ch. 4.2 - Families of Functions (a) Draw the graphs of the...Ch. 4.2 - The Definition of e Illustrate the definition of...Ch. 4.2 - Local Extrema Find the local maximum and minimum...Ch. 4.2 - Local Extrema Find the local maximum and minimum...Ch. 4.2 - Medical Drugs When a certain medical drug is...Ch. 4.2 - Radioactive Decay A radioactive substance decays...Ch. 4.2 - Sky Diving A sky diver jumps from a reasonable...Ch. 4.2 - Mixtures and Concentrations A 50-gal barrel is...Ch. 4.2 - Logistic Growth Animal populations are not capable...Ch. 4.2 - Bird Population The population of a certain...Ch. 4.2 - World Population The relative growth rate of world...Ch. 4.2 - Tree Diameter For a certain type of tree the...Ch. 4.2 - Compound Interest An investment of 7000 is...Ch. 4.2 - Compound Interest An investment of 7000 is...Ch. 4.2 - Compound Interest If 2000 is invested at an...Ch. 4.2 - Compound Interest If 3500 is invested at an...Ch. 4.2 - Compound Interest If 600 is invested at an...Ch. 4.2 - Compound Interest If 8000 is invested in account...Ch. 4.2 - Compound Interest Which of the given interest...Ch. 4.2 - Compound Interest Which of the given interest...Ch. 4.2 - Investment A sum of 5000 is invested at an...Ch. 4.3 - log x is the exponent to which the base 10 must be...Ch. 4.3 - The function f(x) = log9 x is the logarithm...Ch. 4.3 - (a) 53=125,solog= (b) log525=2,so=Ch. 4.3 - Match the logarithmic function with its graph. (a)...Ch. 4.3 - The natural logarithmic function f(x) = ln x has...Ch. 4.3 - The logarithmic function f(x) = ln(x 1) has the...Ch. 4.3 - Logarithmic and Exponential Forms Complete the...Ch. 4.3 - Logarithmic and Exponential Forms Complete the...Ch. 4.3 - Exponential Form Express the equation in...Ch. 4.3 - Exponential Form Express the equation in...Ch. 4.3 - Exponential Form Express the equation in...Ch. 4.3 - Exponential Form Express the equation in...Ch. 4.3 - Exponential Form Express the equation in...Ch. 4.3 - Exponential Form Express the equation in...Ch. 4.3 - Exponential Form Express the equation in...Ch. 4.3 - Exponential Form Express the equation in...Ch. 4.3 - Logarithmic Form Express the equation in...Ch. 4.3 - Logarithmic Form Express the equation in...Ch. 4.3 - Logarithmic Form Express the equation in...Ch. 4.3 - Logarithmic Form Express the equation in...Ch. 4.3 - Logarithmic Form Express the equation in...Ch. 4.3 - Logarithmic Form Express the equation in...Ch. 4.3 - Logarithmic Form Express the equation in...Ch. 4.3 - Logarithmic Form Express the equation in...Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 25....Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 26....Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 27....Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 28....Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 29....Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 30....Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 31....Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 32....Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 33....Ch. 4.3 - Evaluating Logarithms Evaluate the expression. 34....Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Logarithmic Equations Use the definition of the...Ch. 4.3 - Evaluating Logarithms Use a calculator to evaluate...Ch. 4.3 - Evaluating Logarithms Use a calculator to evaluate...Ch. 4.3 - Evaluating Logarithms Use a calculator to evaluate...Ch. 4.3 - Evaluating Logarithms Use a calculator to evaluate...Ch. 4.3 - Graphing Logarithmic Functions Sketch the graph of...Ch. 4.3 - Graphing Logarithmic Functions Sketch the graph of...Ch. 4.3 - Graphing Logarithmic Functions Sketch the graph of...Ch. 4.3 - Graphing Logarithmic Functions Sketch the graph of...Ch. 4.3 - Finding Logarithmic Functions Find the function of...Ch. 4.3 - Finding Logarithmic Functions Find the function of...Ch. 4.3 - Finding Logarithmic Functions Find the function of...Ch. 4.3 - Finding Logarithmic Functions Find the function of...Ch. 4.3 - Graphing Logarithmic Functions Match the...Ch. 4.3 - Graphing Logarithmic Functions Match the...Ch. 4.3 - Graphing Draw the graph of y = 4x, then use it to...Ch. 4.3 - Graphing Draw the graph of y = 3x, then use it to...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Domain Find the domain of the function. 73. f(x) =...Ch. 4.3 - Domain Find the domain of the function. 74. f(x) =...Ch. 4.3 - Domain Find the domain of the function. 75. g(x) =...Ch. 4.3 - Domain Find the domain of the function. 76. g(x) =...Ch. 4.3 - Domain Find the domain of the function. 77. h(x) =...Ch. 4.3 - Domain Find the domain of the function. 78....Ch. 4.3 - Graphing Logarithmic Functions Draw the graph of...Ch. 4.3 - Graphing Logarithmic Functions Draw the graph of...Ch. 4.3 - Graphing Logarithmic Functions Draw the graph of...Ch. 4.3 - Graphing Logarithmic Functions Draw the graph of...Ch. 4.3 - Graphing Logarithmic Functions Draw the graph of...Ch. 4.3 - Graphing Logarithmic Functions Draw the graph of...Ch. 4.3 - Domain of a Composition Find the functions f g...Ch. 4.3 - Domain of a Composition Find the functions f g...Ch. 4.3 - Domain of a Composition Find the functions f g...Ch. 4.3 - Domain of a Composition Find the functions f g...Ch. 4.3 - Rates of Growth Compare the rates of growth of the...Ch. 4.3 - Rates of Growth (a) By drawing the graphs of the...Ch. 4.3 - Family of Functions A family of functions is...Ch. 4.3 - Family of Functions A family of functions is...Ch. 4.3 - Inverse Functions A function f(x) is given, (a)...Ch. 4.3 - Inverse Functions A function f(x) is given, (a)...Ch. 4.3 - Inverse Functions (a) Find the inverse of the...Ch. 4.3 - Absorption of Light A spectrophotometer measures...Ch. 4.3 - Carbon Dating The age of an ancient artifact can...Ch. 4.3 - Bacteria Colony A certain strain of bacteria...Ch. 4.3 - Investment The time required to double the amount...Ch. 4.3 - Charging a Battery The rate at which a battery...Ch. 4.3 - Difficulty of a Task The difficulty in acquiring a...Ch. 4.3 - DISCUSS: The Height of the Graph of a Logarithmic...Ch. 4.3 - DISCUSS: The Googolplex A googol is 10100, and a...Ch. 4.3 - DISCUSS: Comparing Logarithms Which is larger,...Ch. 4.3 - DISCUSS DISCOVER: The Number of Digits in an...Ch. 4.4 - The logarithm of a product of two numbers is the...Ch. 4.4 - The logarithm of a quotient of two numbers is the...Ch. 4.4 - The logarithm of a number raised to a power is the...Ch. 4.4 - We can expand log(x2yz) to get __________.Ch. 4.4 - We can combine 2 log x + log y log z to get...Ch. 4.4 - (a) Most calculators can find logarithms with base...Ch. 4.4 - True or False? 7. (a) log(A + B) is the same as...Ch. 4.4 - (a) logAB is the same as log A log B. (b) logAB...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Families of Functions Draw graphs of the family of...Ch. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Simplify: (log2 5)(log5 7)Ch. 4.4 - A Logarithmic Identity Show that...Ch. 4.4 - Forgetting Use the Law of Forgetting (Example 4)...Ch. 4.4 - Wealth Distribution Vilfredo Pareto (18481923)...Ch. 4.4 - Biodiversity Some biologists model the number of...Ch. 4.4 - Magnitude of Stars The magnitude M of a star is a...Ch. 4.4 - DISCUSS: True or False? Discuss each equation, and...Ch. 4.4 - DISCUSS: Find the Error What is wrong with the...Ch. 4.4 - PROVE: Shifting, Shrinking, and Stretching Graphs...Ch. 4.5 - Lets solve the exponential equation 2ex = 50. (a)...Ch. 4.5 - Lets solve the logarithmic equation...Ch. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Exponential Equations of Quadratic Type Solve the...Ch. 4.5 - Exponential Equations of Quadratic Type Solve the...Ch. 4.5 - Exponential Equations of Quadratic Type Solve the...Ch. 4.5 - Exponential Equations of Quadratic Type Solve the...Ch. 4.5 - Exponential Equations of Quadratic Type Solve the...Ch. 4.5 - Exponential Equations of Quadratic Type Solve the...Ch. 4.5 - Equations Involving Exponential Functions Solve...Ch. 4.5 - Equations Involving Exponential Functions Solve...Ch. 4.5 - Equations Involving Exponential Functions Solve...Ch. 4.5 - Equations Involving Exponential Functions Solve...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Solving Equations Graphically Use a graphing...Ch. 4.5 - Solving Equations Graphically Use a graphing...Ch. 4.5 - Solving Equations Graphically Use a graphing...Ch. 4.5 - Solving Equations Graphically Use a graphing...Ch. 4.5 - Solving Equations Graphically Use a graphing...Ch. 4.5 - Solving Equations Graphically Use a graphing...Ch. 4.5 - Solving Equations Graphically Use a graphing...Ch. 4.5 - Solving Equations Graphically Use a graphing...Ch. 4.5 - More Exponential and Logarithmic Equations Solve...Ch. 4.5 - More Exponential and Logarithmic Equations Solve...Ch. 4.5 - Solving Inequalities Solve the inequality. 79....Ch. 4.5 - Solving Inequalities Solve the inequality. 80. 3 ...Ch. 4.5 - Solving Inequalities Solve the inequality. 81. 2 ...Ch. 4.5 - Solving Inequalities Solve the inequality. 82....Ch. 4.5 - Inverse Functions Find the inverse function of f....Ch. 4.5 - Inverse Functions Find the inverse function of f....Ch. 4.5 - Inverse Functions Find the inverse function of f....Ch. 4.5 - Inverse Functions Find the inverse function of f....Ch. 4.5 - Special Logarithmic Equations Find the value(s) of...Ch. 4.5 - Special Logarithmic Equations Find the value(s) of...Ch. 4.5 - Compound interest A man invests 5000 in an account...Ch. 4.5 - Compound Interest A woman invests 6500 in an...Ch. 4.5 - Compound Interest Find the time required for an...Ch. 4.5 - Compound Interest Nancy wants to invest 4000 in...Ch. 4.5 - Doubling an Investment How long will it take for...Ch. 4.5 - Interest Rate A sum of 1000 was invested for 4...Ch. 4.5 - Radioactive Decay A 15-g sample of radioactive...Ch. 4.5 - Sky Diving The velocity of a sky diver t seconds...Ch. 4.5 - Fish Population A small lake is stocked with a...Ch. 4.5 - Transparency of a Lake Environmental scientists...Ch. 4.5 - Atmospheric Pressure Atmospheric pressure P (in...Ch. 4.5 - Cooling an Engine Suppose youre driving your car...Ch. 4.5 - Electric Circuits An electric circuit contains a...Ch. 4.5 - Learning Curve A learning curve is a graph of a...Ch. 4.5 - DISCUSS: Estimating a Solution Without actually...Ch. 4.5 - DISCUSS DISCOVER: A Surprising Equation Take...Ch. 4.5 - DISCUSS: Disguised Equations Each of these...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Radioactive Radium The half-life of radium-226 is...Ch. 4.6 - Radioactive Cesium The half-life of cesium-137 is...Ch. 4.6 - Radioactive Strontium The half-life of...Ch. 4.6 - Radioactive Radium Radium-221 has a half-life of...Ch. 4.6 - Finding Half-Life If 250 mg of a radioactive...Ch. 4.6 - Radioactive Radon After 3 days a sample of...Ch. 4.6 - Carbon-14 Dating A wooden artifact from an ancient...Ch. 4.6 - Carbon-14 Dating The burial cloth of an Egyptian...Ch. 4.6 - Law of Cooling These exercises use Newtons Law of...Ch. 4.6 - Law of Cooling These exercises use Newtons Law of...Ch. 4.6 - Law of Cooling These exercises use Newtons Law of...Ch. 4.6 - Law of Cooling These exercises use Newtons Law of...Ch. 4.7 - Finding pH The hydrogen ion concentration of a...Ch. 4.7 - Finding pH An unknown substance has a hydrogen ion...Ch. 4.7 - Ion Concentration The pH reading of a sample of...Ch. 4.7 - Ion Concentration The pH reading of a glass of...Ch. 4.7 - Finding pH The hydrogen ion concentrations in...Ch. 4.7 - Ion Concentration in Wine The pH readings for...Ch. 4.7 - pH of Wine If the pH of a wine is too high, say,...Ch. 4.7 - pH of Saliva The pH of saliva is normally in the...Ch. 4.7 - Earthquake Magnitude and Intensity (a) Find the...Ch. 4.7 - Earthquake Magnitude and Intensity (a) Find the...Ch. 4.7 - Earthquake Magnitudes If one earthquake is 20...Ch. 4.7 - Earthquake Magnitudes The 1906 earthquake in San...Ch. 4.7 - Earthquake Magnitudes The Japan earthquake of 2011...Ch. 4.7 - Earthquake Magnitudes The Northridge, California,...Ch. 4.7 - Traffic Noise The intensity of the sound of...Ch. 4.7 - Leaf Blower The intensity of the sound from a...Ch. 4.7 - Hair Dryer The decibel level of the sound from a...Ch. 4.7 - Subway Noise The decibel level of the sound of a...Ch. 4.7 - Hearing Loss from MP3 Players Recent research has...Ch. 4.7 - Comparing Decibel Levels The noise from a power...Ch. 4.7 - PROVE: Inverse Square Law for Sound A law of...Ch. 4 - Let f be the exponential function with base a. (a)...Ch. 4 - Let f be the exponential function f(x) = ax, where...Ch. 4 - If x is large, which function grows faster, f(x) =...Ch. 4 - (a) How is the number e defined? (b) Give an...Ch. 4 - (a) How is loga x defined? (b) Find log3 9. (c)...Ch. 4 - Let f be the logarithmic function f(x) = loga x....Ch. 4 - State the three Laws of Logarithms.Ch. 4 - (a) State the Change of Base Formula. (b) Find...Ch. 4 - (a) What is an exponential equation? (b) How do...Ch. 4 - (a) What is a logarithmic equation? (b) How do you...Ch. 4 - Suppose that an amount P is invested at an...Ch. 4 - Suppose that the initial size of a population is...Ch. 4 - Suppose that the initial mass of a radioactive...Ch. 4 - Suppose that the initial temperature difference...Ch. 4 - What is a logarithmic scale? If we use a...Ch. 4 - (a) What does the pH scale measure? (b) Define the...Ch. 4 - (a) What does the Richter scale measure? (b)...Ch. 4 - (a) What does the decibel scale measure? (b)...Ch. 4 - Evaluating Exponential Functions Use a calculator...Ch. 4 - Evaluating Exponential Functions Use a calculator...Ch. 4 - Evaluating Exponential Functions Use a calculator...Ch. 4 - Evaluating Exponential Functions Use a calculator...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Graphing Exponential and Logarithmic Functions...Ch. 4 - Domain Find the domain of the function. 17....Ch. 4 - Domain Find the domain of the function. 18. g(x) =...Ch. 4 - Domain Find the domain of the function. 19. h(x) =...Ch. 4 - Domain Find the domain of the function. 20. k(x) =...Ch. 4 - Exponential Form Write the equation in exponential...Ch. 4 - Exponential Form Write the equation in exponential...Ch. 4 - Exponential Form Write the equation in exponential...Ch. 4 - Exponential Form Write the equation in exponential...Ch. 4 - Logarithmic Form Write the equation in logarithmic...Ch. 4 - Logarithmic Form Write the equation in logarithmic...Ch. 4 - Logarithmic Form Write the equation in logarithmic...Ch. 4 - Logarithmic Form Write the equation in logarithmic...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Expanding Logarithmic Expressions Expand the...Ch. 4 - Expanding Logarithmic Expressions Expand the...Ch. 4 - Expanding Logarithmic Expressions Expand the...Ch. 4 - Expanding Logarithmic Expressions Expand the...Ch. 4 - Expanding Logarithmic Expressions Expand the...Ch. 4 - Expanding Logarithmic Expressions Expand the...Ch. 4 - Combining Logarithmic Expressions Combine into a...Ch. 4 - Combining Logarithmic Expressions Combine into a...Ch. 4 - Combining Logarithmic Expressions Combine into a...Ch. 4 - Combining Logarithmic Expressions Combine into a...Ch. 4 - Combining Logarithmic Expressions Combine into a...Ch. 4 - Combining Logarithmic Expressions Combine into a...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential and Logarithmic Equations Solve the...Ch. 4 - Exponential Equations Use a calculator to find the...Ch. 4 - Exponential Equations Use a calculator to find the...Ch. 4 - Exponential Equations Use a calculator to find the...Ch. 4 - Exponential Equations Use a calculator to find the...Ch. 4 - Local Extrema and Asymptotes Draw a graph of the...Ch. 4 - Local Extrema and Asymptotes Draw a graph of the...Ch. 4 - Local Extrema and Asymptotes Draw a graph of the...Ch. 4 - Local Extrema and Asymptotes Draw a graph of the...Ch. 4 - Solving Equations Find the solutions of the...Ch. 4 - Solving Equations Find the solutions of the...Ch. 4 - Solving Inequalities Solve the inequality...Ch. 4 - Solving Inequalities Solve the inequality...Ch. 4 - Increasing and Decreasing Use a graph of f(x) = ex...Ch. 4 - Equation of a Line Find an equation of the line...Ch. 4 - Change of Base Use the Change of Base Formula to...Ch. 4 - Change of Base Use the Change of Base Formula to...Ch. 4 - Change of Base Use the Change of Base Formula to...Ch. 4 - Change of Base Use the Change of Base Formula to...Ch. 4 - Comparing Logarithms Which is larger, log4 258 or...Ch. 4 - Inverse Function Find the inverse of the function...Ch. 4 - Compound Interest If 12,000 is invested at an...Ch. 4 - Compound Interest A sum of 5000 is invested at an...Ch. 4 - Compound Interest A money market account pays 5.2%...Ch. 4 - Compound Interest A retirement savings plan pays...Ch. 4 - APY Determine the annual percentage yield (APY)...Ch. 4 - APY Determine the annual percentage yield (APY)...Ch. 4 - Cat Population The stray-cat population in a small...Ch. 4 - Bacterial Growth A culture contains 10,000...Ch. 4 - Radioactive Decay Uranium-234 has a half-life of...Ch. 4 - Radioactive Decay A sample of bismuth-210 decayed...Ch. 4 - Radioactive Decay The half-life of radium-226 is...Ch. 4 - Radioactive Decay The half-life of palladium-100...Ch. 4 - Bird Population The graph shows the population of...Ch. 4 - Law of Cooling A car engine runs at a temperature...Ch. 4 - pH The hydrogen ion concentration of fresh egg...Ch. 4 - pH The pH of lime juice is 1.9. Find the hydrogen...Ch. 4 - Richter Scale If one earthquake has magnitude 6.5...Ch. 4 - Decibel Scale The drilling of a jackhammer was...Ch. 4 - Sketch the graph of each function, and state its...Ch. 4 - Find the domain of the function. (a) f(t) = ln(2t ...Ch. 4 - (a) Write the equation 62x = 25 in logarithmic...Ch. 4 - Find the exact value of the expression. (a) 10log...Ch. 4 - Use the Laws of Logarithms to expand the...Ch. 4 - Use the Laws of Logarithms to combine the...Ch. 4 - Find the solution of the exponential equation,...Ch. 4 - Solve the logarithmic equation for x. (a) log(2x)...Ch. 4 - Use the Change of Base Formula to evaluate log12...Ch. 4 - The initial size of a culture of bacteria is 1000....Ch. 4 - Suppose that 12,000 is invested in a savings...Ch. 4 - The half-life of krypton-91 (91Kr) is 10 s. At...Ch. 4 - An earthquake measuring 6.4 on the Richter scale...Ch. 4 - U.S. Population The U.S. Constitution requires a...Ch. 4 - A Falling Ball In a physics experiment a lead ball...Ch. 4 - Half-Life of Radioactive Iodine A student is...Ch. 4 - The Beer-Lambert Law As sunlight passes through...Ch. 4 - Experimenting with Forgetting Curves Every one of...Ch. 4 - Modeling the Species-Area Relation The table gives...Ch. 4 - Auto Exhaust Emissions A study by the U.S. Office...Ch. 4 - Exponential or Power Model? Data points (x, y) are...Ch. 4 - Exponential or Power Model? Data points (x, y) are...Ch. 4 - Logistic Population Growth The table and scatter...

Find more solutions based on key concepts

Show solutions You put some ice cubes in a glass, fill the glass with cold water, and then let the glass sit on a table. Descr...

Single Variable Calculus: Early Transcendentals, Volume I

Sketching the Graph of an Exponential Function In Exercises 27-40, sketch the graph of the function. y=ex

Calculus: Early Transcendental Functions

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Applied Calculus

Match the function (a) with its graph (labeled AF below) and (b) with its contour map (labeled IVI). Give reaso...

Multivariable Calculus

Evaluating Basic Limits In Exercises 13-20, find the limit. See Example 3. limx7x2

Calculus: An Applied Approach (MindTap Course List)

Suppose that the directional derivatives of f(x, y) are known at a given point in two nonparallel directions gi...

Calculus: Early Transcendentals

Evaluate expressions in Exercises 3756, rounding your answer to four significant digits where necessary. 2516

Finite Mathematics and Applied Calculus (MindTap Course List)

SOC A random sample of 423 Asian Americans drawn from the population of a particular state has finished an aver...

Essentials Of Statistics

A researcher is curious about the average distance traveled by Canada geese during peak fall migration in the s...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or gi...

Calculus (MindTap Course List)

For the following scores, the smallest value is X = 13 and the largest value is X = 52. Place the scores in a g...

Statistics for The Behavioral Sciences (MindTap Course List)

How would you remove the discontinuity of f? In other words, how would you define f(2) in order to make f conti...

Single Variable Calculus

U.S. Health-Care Costs The U.S. health-care costs per capita (in dollars) from 2001 through 2011 can be approxi...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Solve the equations in Exercises 126. 2x3x12x+3x+1=0

Finite Mathematics

Expand Your knowledge: Outliers Some data include values so high or so low that they seem to stand apart from t...

Understanding Basic Statistics

Consider the next 1000 95% CIs for that a statistical consultant will obtain for various clients. Suppose the ...

Probability and Statistics for Engineering and the Sciences

32. Cost Suppose a company has two separate plants that manufacture the same item. Suppose x is the amount prod...

Mathematical Applications for the Management, Life, and Social Sciences

In Exercises 17 to 22, use proportions to solve each problem. The secretarial pool 15 secretaries in all on one...

Elementary Geometry For College Students, 7e

Use the following financial information to prepare a balance sheet as of December 31, 2016. for Keystone Auto R...

Contemporary Mathematics for Business & Consumers

In Exercises 15 to 18, show that the given set is an infinite set by placing it in a one-to-one correspondence ...

Mathematical Excursions (MindTap Course List)

Simplify the algebraic expressions in Problems 1-14 by com- bining similar terms. Objective 1 3a2+7b2+9a22b2

Intermediate Algebra

Use the map in Illustration 1 to find the approximate air distance between each pair of cities: ILLUSTRATION 1 ...

Elementary Technical Mathematics

The Fibonacci sequence was defined in Section 11.1 by the equations f1=1,f2=1,fn=fn1+fn2n3 Show that each of th...

Single Variable Calculus: Early Transcendentals

Finding the Domain and Range of a Function In Exercises 13-22, find the domain and range of the function. f(x)=...

Calculus of a Single Variable

Finding an Indefinite Integral In Exercises 79-84, find the indefinite integral. 17x2dx

Calculus: Early Transcendental Functions (MindTap Course List)

For Questions 1 through 8, fill in the blank with an appropriate word. The dot product of two vectors is also e...

Trigonometry (MindTap Course List)

Label each of the following statements as either true or false. If (a,n)=1, then a1(modn).

Elements Of Modern Algebra

Suppose in an estimation of a root of f(x) = 0 we make an initial guess x1 and it turns out that f'′(x1) = 0. W...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

For what value of n is the nth partial sum within 0.01 of the value of ? (Choose the smallest such n.)
n = 4
n ...

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercise 27 and 28, use the given angle R and the line segment of length b. Construct the right triangle in ...

Elementary Geometry for College Students

Sales of Plasma TVs The records of Ace Electronics show that of the plasma TVs sold by the company, 26 were man...

Finite Mathematics for the Managerial, Life, and Social Sciences

Analyzing the Graph of a Function In Exercises 37-44, analyze and sketch a graph of the function over the given...

Calculus (MindTap Course List)

Finding a Directional DerivativeIn Exercises 2528, use the gradient to find the directional derivative of the f...

Multivariable Calculus

In an experiment examining human memory, two groups of participants are used. One group is allowed 5 minutes to...

Research Methods for the Behavioral Sciences (MindTap Course List)

The New York City Housing and Vacancy Survey showed a total of 59,324 rent-controlled housing units and 236,263...

Statistics for Business & Economics, Revised (MindTap Course List)

Describe the two nonexperimental nonequivalent group designs (differential research and the posttest-only noneq...

Research Methods for the Behavioral Sciences (MindTap Course List)

Is the polynomial x3+1 prime?

College Algebra (MindTap Course List)

The admissions officer for Clearwater College developed the following estimated regression equation relating th...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Express the common fractions as decimal fractions. Express the answer to 4 decimal places. 26. 12

Mathematics For Machine Technology

The paper referenced in Exercise CR5.9 also gave data on sodium content (in milligrams per kilogram) of 10 choc...

Introduction To Statistics And Data Analysis