Write each equation in its equivalent logarithmic form. ∛8 = 2

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. g(x) = (3/2)^x

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 3^1-x=1/27

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln(e²/5)

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log_b x³

Write each equation in its equivalent exponential form. log₃ 81 = y

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. h(x) = (1/2)^x

Write each equation in its equivalent logarithmic form. 13² = x

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 6^(x−3)/4=√6

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 4^x=1/√2

Write each equation in its equivalent logarithmic form. b³ = 1000

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log N^-6

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = (0.6)^x

In Exercises 16–18, write each equation in its equivalent logarithmic form. 13^y = 874

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\ln \sqrt[5]{x}$

Write each equation in its equivalent logarithmic form. 7^y = 200

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 8^(x+3)=16^(x−1)

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options:

$f(x) = 3^x, \quad g(x) = 3^{x-1}, \quad h(x) = 3^x - 1, \\ f(x) = -3^x, \quad G(x) = 3^{-x}, \quad H(x) = -3^{-x}.$

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log5 (1/5)

Evaluate each expression without using a calculator. log₄ 16

The graph of an exponential function is given. Select the function for each graph from the following options:

$f(x) = 3^x, \quad g(x) = 3^{x-1}, \quad h(x) = 3^x - 1, \\ f(x) = -3^x, \quad G(x) = 3^{-x}, \quad H(x) = -3^{-x}.$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log_b (x² y)

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. e^(x+1)=1/e

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log16 4

Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 10^x=3.91

Evaluate each expression without using a calculator. log₂ 64

The graph of an exponential function is given. Select the function for each graph from the following options:

$f(x) = 3^x, \quad g(x) = 3^{x-1}, \quad h(x) = 3^x - 1, \\ f(x) = -3^x, \quad G(x) = 3^{-x}, \quad H(x) = -3^{-x}.$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ${\log }_4\left(\frac{\sqrt{x}}{64}\right)$

Evaluate each expression without using a calculator. log₃ 27