Chapter 9

Write each as an exponential equation. See Example 1. $$ \log _{6} 36=2 $$

Solve each equation. Give an exact solution and approximate the solution to four decimal places. See Example 1. $$ 3^{x}=6 $$

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1 . $$ \log _{5} 2+\log _{5} 7 $$

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function by switching coordinates, or inputs and outputs. \(f=\\{(-1,-1),(1,1),(0,2),(2,0)\\}\)

For the functions \(f\) and \(g,\) find \(a .(f+g)(x), b .(f-g)(x)\) \(c .(f \cdot g)(x),\) and \(d .\left(\frac{f}{g}\right)(x) .\) $$f(x)=x-7, g(x)=2 x+1$$

Use a calculator to approximate each logarithm to four decimal places. See Examples I and 5. \(\log 8\)

Graph each exponential function. See Examples 1 through \(3 .\) $$ y=5^{x} $$

Write each as an exponential equation. See Example 1. $$ \log _{2} 32=5 $$

Solve each equation. Give an exact solution and approximate the solution to four decimal places. See Example 1. $$ 4^{x}=7 $$

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1 . $$ \log _{3} 8+\log _{3} 4 $$

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function by switching coordinates, or inputs and outputs. \(g=\\{(8,6),(9,6),(3,4),(-4,4)\\}\)

For the functions \(f\) and \(g,\) find \(a .(f+g)(x), b .(f-g)(x)\) \(c .(f \cdot g)(x),\) and \(d .\left(\frac{f}{g}\right)(x) .\) $$f(x)=x+4, g(x)=5 x-2$$

Use a calculator to approximate each logarithm to four decimal places. See Examples I and 5. \(\log 6\)

Graph each exponential function. See Examples 1 through \(3 .\) $$ y=4^{x} $$

Write each as an exponential equation. See Example 1. $$ \log _{3} \frac{1}{27}=-3 $$

Use a calculator to approximate each logarithm to four decimal places. See Examples I and 5. \(\log 2.31\)

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1 . $$ \log _{4} 9+\log _{4} x $$

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function by switching coordinates, or inputs and outputs. \(h=\\{(10,10)\\}\)

For the functions \(f\) and \(g,\) find \(a .(f+g)(x), b .(f-g)(x)\) \(c .(f \cdot g)(x),\) and \(d .\left(\frac{f}{g}\right)(x) .\) $$ f(x)=x^{2}+1, g(x)=5 x $$

Solve each equation. Give an exact solution and approximate the solution to four decimal places. See Example 1. $$ 3^{2 x}=3.8 $$

Write each as an exponential equation. See Example 1. $$ \log _{5} \frac{1}{25}=-2 $$

Solve each equation. Give an exact solution and approximate the solution to four decimal places. See Example 1. $$ 5^{3 x}=5.6 $$

Use a calculator to approximate each logarithm to four decimal places. See Examples I and 5. \(\log 4.86\)

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1 . $$ \log _{2} x+\log _{2} y $$

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function by switching coordinates, or inputs and outputs. \(r=\\{(1,2),(3,4),(5,6),(6,7)\\}\)

For the functions \(f\) and \(g,\) find \(a .(f+g)(x), b .(f-g)(x)\) \(c .(f \cdot g)(x),\) and \(d .\left(\frac{f}{g}\right)(x) .\) $$f(x)=x^{2}-2, g(x)=3 x$$

Practice using the exponential growth formula by completing the table below. Round final amounts to the nearest whole. See Example 1. $$ \begin{array}{|c|c|c|c|} \hline \text {Original } & {\text {Growth Rate per}} & {\text {Number}} & {\text {Final A mount after } x \text {Years}} \\ {\text {Amount}} & {\text {Year}} & {\text {of Years, } x} & {\text {of Growth}} \\ \hline 1000 & {47 \%} & {19} \\ \hline \end{array} $$

Graph each exponential function. See Examples 1 through \(3 .\) $$ y=3^{x}-1 $$

Write each as an exponential equation. See Example 1. $$ \log _{10} 1000=3 $$

Solve each equation. Give an exact solution and approximate the solution to four decimal places. See Example 1. $$ 2^{x-3}=5 $$

Use a calculator to approximate each logarithm to four decimal places. See Examples I and 5. \(\ln 2\)

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1 . $$ \log _{6} x+\log _{6}(x+1) $$

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function by switching coordinates, or inputs and outputs. \(f=\\{(11,12),(4,3),(3,4),(6,6)\\}\)

For the functions \(f\) and \(g,\) find \(a .(f+g)(x), b .(f-g)(x)\) \(c .(f \cdot g)(x),\) and \(d .\left(\frac{f}{g}\right)(x) .\) $$f(x)=\sqrt[3]{x}, g(x)=x+5$$

Practice using the exponential growth formula by completing the table below. Round final amounts to the nearest whole. See Example 1. $$ \begin{array}{|c|c|c|c|} \hline \text {Original } & {\text {Growth Rate per}} & {\text {Number}} & {\text {Final A mount after } x \text {Years}} \\ {\text {Amount}} & {\text {Year}} & {\text {of Years, } x} & {\text {of Growth}} \\ \hline 17 & {29 \%} & {28} \\ \hline \end{array} $$

Write each as an exponential equation. See Example 1. $$ \log _{10} 10=1 $$

Solve each equation. Give an exact solution and approximate the solution to four decimal places. See Example 1. $$ 8^{x-2}=12 $$

Use a calculator to approximate each logarithm to four decimal places. See Examples I and 5. \(\ln 3\)

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1 . $$ \log _{5} y^{3}+\log _{5}(y-7) $$

Determine whether each function is a one-to-one function. If it is one-to-one, list the inverse function by switching coordinates, or inputs and outputs. \(g=\\{(0,3),(3,7),(6,7),(-2,-2)\\}\)

For the functions \(f\) and \(g,\) find \(a .(f+g)(x), b .(f-g)(x)\) \(c .(f \cdot g)(x),\) and \(d .\left(\frac{f}{g}\right)(x) .\) $$f(x)=\sqrt[3]{x}, g(x)=x-3$$

Write each as an exponential equation. See Example 1. $$ \log _{9} x=4 $$

Solve each equation. Give an exact solution and approximate the solution to four decimal places. See Example 1. $$ 9^{x}=5 $$

Practice using the exponential decay formula by completing the table below. Round final amounts to the nearest whole. See Example 2. $$ \begin{array}{|c|c|c|c|} \hline \text { Original } & {\text {Decay Rate per }} & {\text { Number }} & {\text { Final Amount after } x \text { Years }} \\ {\text { Amount }} & {\text { Year }} & {\text { of Years, } x} & {\text { of Decay }} \\ \hline 305 & {5 \%} & {8} \\ \hline \end{array} $$

Use a calculator to approximate each logarithm to four decimal places. See Examples I and 5. \(\ln 0.0716\)

Write each sum as a single logarithm. Assume that variables represent positive numbers. See Example 1 . $$ \log _{10} 5+\log _{10} 2+\log _{10}\left(x^{2}+2\right) $$

Graph each exponential function. See Examples 1 through \(3 .\) $$ y=\left(\frac{1}{2}\right)^{x}-2 $$

For the functions \(f\) and \(g,\) find \(a .(f+g)(x), b .(f-g)(x)\) \(c .(f \cdot g)(x),\) and \(d .\left(\frac{f}{g}\right)(x) .\) $$f(x)=-3 x, g(x)=5 x^{2}$$

Write each as an exponential equation. See Example 1. $$ \log _{8} y=7 $$

Solve each equation. Give an exact solution and approximate the solution to four decimal places. See Example 1. $$ 3^{x}=11 $$