Using the One-to-One Property In Exercises 29-32, use the One-to-One Property to solve the equation for x. 30. log (x - 3) - log, 9 29. log, (x + 1) - log, 6 31. log 11 - log(x + 7) 32. log(r + 6x) - log 27

Q: Using Properties of Logarithms In Exercises 87 and $88,$ use the properties of logarithms to…

A: NOTE- AS WE ARE ALLOWED TO ANSWER MAXIMUM THREE SUBPARTS IN ONE QUESTION SO, I HAVE ANSWERED FIRST…

Q: The logarithm of a quotient of two numbers is the same as the  ---Select--- quotient sum difference…

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Q: Solving a Logarithmic Equation InExercises 47–62, solve the logarithmicequation algebraically.…

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Q: Using Properties of Logarithms In Exercises 87 and 88 , use the properties of logarithms to…

A: Given: ln2=0.6931ln3=1.0986(a)  ln(6)=?(b)  ln23=?(c)  ln(81)=?(d)  ln(3)=?

Q: Writing an Exponential Equation In Exercises7–10, write the logarithmic equation in exponentialform.…

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Q: Solving a Simple Equation In Exercises7–16, solve for x.

A: 7) Given that, 4x=16 Simplification: Since we have, 4x=16 So 4x=42x=2         If am=an⇒m=n Hence x =…

Q: log32+log32-log35-log35 convert to single log form

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Q: Using the Change-of-Base Formula In Exercises97–100, use the change-of-base formula to rewrite…

A: NOTE- AS WE ARE ALLOWED TO ANSWER THREE SUBPARTS IN ONE SESSION. SO, I HAVE ANSWERED FIRST THREE FOR…

Q: Expand: 5x3 1.) In

A: log(ab)=log(a)-log(b)log(ab)=log(a)+log(b)log(am)=m×log(a)   (By our guidelines, we have to do only…

Q: Introduction: Overall plan of the work with reference to the discussion about the meaning and…

A: (a) Qudratic equationIf the maximum power of a monomial zn anequation is 2, then zt is a quadratic…

Q: Sketching the Graph of a LogarithmicFunction In Exercises 41–48, find thedomain, x-intercept, and…

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Q: Graphing a Natural Logarithmic Function InExercises 71–74, use a graphing utility to graph…

A: Part(a) Given function is fx=lnx-1

Q: Find the domain of the logarithmic function. y=log2 (x2-5x-36) Choose the domain of the function.…

A: We have to find domain

Q: (a) Combine using laws of logarithms and evaluate log2 25 – log2 5 – log2 40

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Q: Evaluating a Logarithm In Exercises15–20, evaluate the logarithm at the givenvalue of x without…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3. Exploration of the Quotient Law of Logarithms. Make and test a conjecture about the quotient law…

A: loga(x) loga(y) loga(xy) log232=log225=5 log28=log223=3 log2328=log24=log222=2 log327=log333=3…

Q: Depreciation: The price p, in dollars, of a Honda Civic EX-L Sedan that is x years old is modeled by…

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Q: population of a city is 85,000 and increases by 2.4% each year. Which exponential function models…

A: The given question is taken from the compound interest in which we have to find the function in term…

Q: Carbon dating is one of the methods used to determine the age of an artifact by determining the…

A: Use the formula for the age calculation from carbon-14 involving exponential function.

Q: Using Properties of Logarithms In Exercises33–40, approximate the logarithm using the propertiesof…

A: "Since you have posted question with multiple subparts, we will solve first three subparts for you.…

Q: Find the domain, vertical asymptote, and x-intercept of the logarithmic function. (Enter your domain…

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Q: Finding the Best Model. In Exercises 5–16, construct a scatterplot and identify the mathematical…

A: The data shows the mean annual temperatures of the earth for each decade beginning with 1880s.…

Q: Radiocarbon dating: Carbon-14 is a radioactive isotope of carbon that decays by emitting a beta…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: 5. Explain how the formula for differentiating the natural ex- ponential function is a special case…

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Q: 8. Between what two consecutive integers must the value of log, 7342 lie? Justify your answer.

A: Consider the given logarithmic expression, log47342 since, the number 7342 lies between, 46=4096 and…

Q: A tumor is injected with 0.9 grams of iodine-125, which has a decay rate of 1.15% per day. Write an…

A: Solution:-

Q: Finding a Derivative of an ExponentialFunction In Exercises 57–72, find the derivativeof the…

A: we have to find the derivative of the exponential function. y=e5x

Q: Find a formula for the exponential function passing through the points (-3,- -) and (3,320) 64

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Q: Matching a Logarithmic Function with Its GraphIn Exercises 37–40, use the graph of g(x) = log3 x…

A: 37. The given function is fx=log3x+2 Let us assume gx=log3x. So, fx=gx+2 The relation between f and…

Q: Natural Logarithmic Function Explain why In x is positive for x > 1 and negative for 0 < x < 1.

A: The definition of logarithm function is,                   ln x = ∫1x  1tdt , x&gt;0…

Q: Condensing a Logarithmic ExpressionIn Exercises 61–76, condense the expressionto the logarithm of a…

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Q: Critically outline with practical examples and illustrations of hoe to differentiate and integrate…

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Q: Submit Test Ouestion 3 of 15- The graph of a linear function and an exponential function is shown…

A: As can be seen from the graph, the linear function exceeds the exponential function for values of x…

Q: Graphing Exponential and LogarithmicFunctions In Exercises 33–36, sketch thegraphs of f and g in the…

A: Given: 33.  f(x)=7x,  g(x)=log7x34.  f(x)=5x,  g(x)=log5x35.  f(x)=6x,  g(x)=log6x36.  f(x)=10x,…

Q: The revenue of Apple® went from $54.5 billion in 2013 to $74.6 billion50 in 2015. Find an…

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Q: Graphing a Natural Exponential Function InExercises 41–44, use a graphing utility to graph…

A: Part(a) Given exponential function is st=2e0.5t

Q: true or false? explain log (2/3) = (log2)/(log3)

A: The given expression is: log23=log2log3 The given expression is true or false?

Q: log(3x-1)=log(4-x)

A: The given equation is log (3x–1) = log (4–x).

Q: Using Properties of Logarithms InExercises 13–18, use the properties oflogarithms to write the…

A: Answer(13): The given logarithm expression is: log335 Since, 35=5×7 So, log335=log35×7 Now, apply…

Q: 4 in the form log,x for b = 7. State the value of x, and verify your answer using a calcula Write…

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Q: 9. Between what two consecutive integers must the value of log, (00) lie? Justify your answer.

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Q: Determining the Domain Algebraically a. Determine the domain of ƒ(x)=log(2x–7).

A: We have to find the domain of given function

Q: Comparing Logarithmic Quantities In Exercises77 and 78, determine which (if any) of the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The number of cell phone subscribers has been growing exponentially for some time. According to…

A: Exponential model of growth is given by, p(t) = abt thousand where t is number of years after 2000 a…

Q: True or False? In Exercises 89–92, rewrite eachverbal statement as an equation. Then decide…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Evaluating a Natural ExponentialFunction In Exercises 33–36, evaluate thefunction at the given value…

A: "Since, you have asked a question with multiple subparts , we will solve the first three subparts…

Q: (i). To find a logarithm of a number, two case must be considered. Critically outline these cases in…

A: i) If a is any number such that a &gt; 0 and a ≠ 1 and x &gt; 0 then, y = loga x is equivalent to…

Q: 1) log2x = 5 2) log, x <3

A:

Q: Logarithms In Exercises 33–40, approximate the logarithm using the properties of logarithms, given…

A: Consider the following expressions: logb2≈0.3562logb3≈0.5646logb5≈0.8271…

Q: Evaluating a Common Logarithm on a CalculatorIn Exercises 21–24, use a calculator to evaluatef(x) =…

A: Given, 21) x=78 Now find: f(x)=log(x) Now substitute the value of "x" we get, f(x)=log78 we know…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.