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Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759

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Chapter
Section
BuyFindarrow_forward

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759
Chapter 4.7, Problem 1E
Textbook Problem
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Finding pH The hydrogen ion concentration of a sample of each substance is given. Calculate the pH of the substance.

  1. (a) Lemon juice: [H+] = 5.0 × 10−3 M
  2. (b) Tomato juice: [H+] = 3.2 × 10−4 M
  3. (c) Seawater: [H+] = 5.0 × 10−9 M

(a)

To determine

To calculate: The pH of the lemon juice for which the hydrogen ions concentration in the lemon juice sample is [H+]=5.0×103M .

Explanation of Solution

Formula used:

The pH of any solution is defined by pH=log[H+] , where [H+] is the concentration of the hydrogen ions measured in moles per liter (M).

Calculation:

It is given that the concentration of the hydrogen ions in the lemon juice solution is [H+]=5.0×103M .

Substitute [H+]=5.0×103 in the formula pH=log[H+] and find the pH of the lemon juice as follows

(b)

To determine

To calculate: The pH of the tomato juice for which the hydrogen ions concentration in the tomato juice sample is [H+]=3.2×104M .

(c)

To determine

To calculate: The pH of the seawater where the hydrogen ions concentration in the seawater sample is [H+]=5.0×109M .

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Chapter 4 Solutions

Precalculus: Mathematics for Calculus (Standalone Book)
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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 - 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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...

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