Ch. 4 - Exponential and Logarithmic Functions
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Problem 1
In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 1.
Problem 1
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 2^3.4Problem 1
In Exercises 1–8, write each equation in its equivalent exponential form. 4 = log₂ 16Problem 1
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log5 (7 × 3)Problem 1
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^x=64Problem 3
In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 3.
Problem 3
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 5^x=125Problem 3
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3^√5Problem 3
In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log3 xProblem 3
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log7 (7x)Problem 4
In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log9 xProblem 5
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^2x−1=32Problem 5
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 4^-1.5Problem 5
In Exercises 1–8, write each equation in its equivalent exponential form. 5= logb 32Problem 5
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(1000x)Problem 7
In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = 3^x and g(x) = -3^xProblem 7
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 4^2x−1=64Problem 7
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^2.3Problem 7
In Exercises 1–8, write each equation in its equivalent exponential form. log6 216 = yProblem 7
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log7 (7/x)Problem 9
In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = e^x and g(x) = 2e^(x/2)Problem 9
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 32^x=8Problem 9
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^-0.95Problem 9
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(x/100)Problem 10
Use the compound interest formulas to solve Exercises 10–11. Suppose that you have $5000 to invest. Which investment yields the greater return over 5 years: 1.5% compounded semiannually or 1.45% compounded monthly?Problem 10
In Exercises 9–20, write each equation in its equivalent logarithmic form. 5^4 = 625Problem 11
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 9^x=27Problem 11
In Exercises 9–20, write each equation in its equivalent logarithmic form. 2^-4 = 1/16Problem 11
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (64/y)Problem 11
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = 4^x
