Chapter 12

Write each equation in its equivalent logarithmic form. $$13^{2}=x$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$7^{\frac{x-2}{6}}=\sqrt{7}$$

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

Write each equation in its equivalent logarithmic form. $$15^{2}=x$$

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

Write each equation in its equivalent logarithmic form. $$b^{3}=1000$$

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 unility to confirm your hand-drawn graph. $$f(x)=4^{x}$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$9^{x}=\frac{1}{\sqrt[3]{3}}$$

Write each equation in its equivalent logarithmic form. $$b^{3}=343$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log M^{-8}$$

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

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$e^{x}=5.7$$

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

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

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

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$e^{x}=0.83$$

Write each equation in its equivalent logarithmic form. $$8^{y}=300$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\ln \sqrt[7]{x}$$

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

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of 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. $$\log _{4} 16$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{b}\left(x^{2} y\right)$$

Graph each function by making a table of coordinates. If applicable, use a graphing unility to confirm your hand-drawn graph. $$h(x)=\left(\frac{1}{2}\right)^{x}$$

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$10^{x}=8.07$$

Evaluate each expression without using a calculator. $$\log _{7} 49$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{b}\left(x y^{3}\right)$$

Graph each function by making a table of coordinates. If applicable, use a graphing unility to confirm your hand-drawn graph. $$h(x)=\left(\frac{1}{3}\right)^{x}$$

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$5^{x}=17$$

Evaluate each expression without using a calculator. $$\log _{2} 64$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{4}\left(\frac{\sqrt{x}}{64}\right)$$

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

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$19^{x}=143$$

Evaluate each expression without using a calculator. $$\log _{3} 27$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{5}\left(\frac{\sqrt{x}}{25}\right)$$

Graph each function by making a table of coordinates. If applicable, use a graphing unility to confirm your hand-drawn graph. $$f(x)=(0.8)^{x}$$

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$5 e^{x}=25$$

Evaluate each expression without using a calculator. $$\log _{5} \frac{1}{5}$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{6}\left(\frac{36}{\sqrt{x+1}}\right)$$

Graph functions \(f\) and \(g\) in the same rectangular coordinate system. Select integers from \(-2\) to 2 , inclusive, for \(x\). Then describe how the graph of g is related to the graph of \(f .\) If applicable, use a graphing utility to confirm your hand-drawn graphs. $$f(x)=2^{x} \text { and } g(x)=2^{x+1}$$

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$9 e^{x}=99$$

Evaluate each expression without using a calculator. $$\log _{6} \frac{1}{6}$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{8}\left(\frac{64}{\sqrt{x+1}}\right)$$

Graph functions \(f\) and \(g\) in the same rectangular coordinate system. Select integers from \(-2\) to 2 , inclusive, for \(x\). Then describe how the graph of g is related to the graph of \(f .\) If applicable, use a graphing utility to confirm your hand-drawn graphs. $$f(x)=2^{x} \quad \text { and } \quad g(x)=2^{x+2}$$

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$3 e^{5 x}=1977$$

Evaluate each expression without using a calculator. $$\log _{2} \frac{1}{8}$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $$\log _{b}\left(\frac{x^{2} y}{z^{2}}\right)$$

Graph functions \(f\) and \(g\) in the same rectangular coordinate system. Select integers from \(-2\) to 2 , inclusive, for \(x\). Then describe how the graph of g is related to the graph of \(f .\) If applicable, use a graphing utility to confirm your hand-drawn graphs. $$f(x)=2^{x} \text { and } g(x)=2^{x-2}$$

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$4 e^{7 x}=10,273$$

Evaluate each expression without using a calculator. $$\log _{3} \frac{1}{9}$$