Chapter 4

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$2^{x}=64$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log _{5}(7 \cdot 3)\)

Write each equation in its equivalent exponential form. $$4=\log _{2} 16$$

Approximate each number using a calculator. Round your answer to three decimal places. $$2^{3.4}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$3^{x}=81$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log _{8}(13 \cdot 7)\)

Write each equation in its equivalent exponential form. $$6=\log _{2} 64$$

Approximate each number using a calculator. Round your answer to three decimal places. $$3^{2.4}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{x}=125$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log _{7}(7 x)\)

Write each equation in its equivalent exponential form. $$2=\log _{3} x$$

Approximate each number using a calculator. Round your answer to three decimal places. $$3^{\sqrt{5}}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{x}=625$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log _{9}(9 x)\)

Write each equation in its equivalent exponential form. $$2=\log _{9} x$$

Approximate each number using a calculator. Round your answer to three decimal places. $$5^{\sqrt{3}}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$2^{2 x-1}=32$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log (1000 x)\)

Write each equation in its equivalent exponential form. $$5=\log _{b} 32$$

Approximate each number using a calculator. Round your answer to three decimal places. $$4^{-1.5}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$3^{2 x+1}=27$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log (10,000 x)\)

Write each equation in its equivalent exponential form. $$3=\log _{b} 27$$

Approximate each number using a calculator. Round your answer to three decimal places. $$6^{-1.2}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$4^{2 x-1}=64$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log _{7}\left(\frac{7}{x}\right)\)

Write each equation in its equivalent exponential form. $$\log _{6} 216=y$$

Approximate each number using a calculator. Round your answer to three decimal places. $$e^{2.3}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{3 x-1}=125$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log _{9}\left(\frac{9}{x}\right)\)

Write each equation in its equivalent exponential form. $$\log _{5} 125=y$$

Approximate each number using a calculator. Round your answer to three decimal places. $$e^{3.4}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$32^{x}=8$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log \left(\frac{x}{100}\right)\)

Write each equation in its equivalent logarithmic form. $$2^{3}=8$$

Approximate each number using a calculator. Round your answer to three decimal places. $$e^{-0.95}$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log \left(\frac{x}{1000}\right)\)

Write each equation in its equivalent logarithmic form. $$5^{4}=625$$

Approximate each number using a calculator. Round your answer to three decimal places. $$e^{-0.75}$$

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$f(x)=4^{x}$$

Write each equation in its equivalent logarithmic form. $$2^{-4}=\frac{1}{16}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$125^{x}=625$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\log _{5}\left(\frac{125}{y}\right)\)

Write each equation in its equivalent logarithmic form. $$5^{-3}=\frac{1}{125}$$

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$f(x)=5^{x}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$3^{1-x}=\frac{1}{27}$$

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$g(x)=\left(\frac{3}{2}\right)^{x}$$

Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \(\ln \left(\frac{e^{2}}{5}\right)\)

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{2-x}=\frac{1}{125}$$

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$g(x)=\left(\frac{4}{3}\right)^{x}$$