Chapter 12

Solve each equation. Give an exact solution and a four-decimal-place approximation. $$ 3^{x}=6 $$

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

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

Use a calculator to approximate each logarithm to four decimal places. $$ \log 8 $$

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

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. \(g=\\{(0,3),(3,7),(6,7),(-2,-2)\\}\)

Graph each exponential function. $$ y=5^{x} $$

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

Solve each equation. Give an exact solution and a four-decimal-place approximation. $$ 4^{x}=7 $$

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

Practice using the exponential growth formula by completing the table below. Round final amounts to the nearest whole. $$ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text { Original } \\ \text { Amount } \end{array} & \begin{array}{c} \text { Growth } \\ \text { Rate per Year } \end{array} & \begin{array}{c} \text { Number } \\ \text { of Years, } \boldsymbol{x} \end{array} & \begin{array}{c} \text { Final Amount after } \\ \boldsymbol{x} \text { Years of Growth } \end{array} \\ \hline 402 & 7 \% & 5 & \\ \hline \end{array} $$

Use a calculator to approximate each logarithm to four decimal places. $$ \log 6 $$

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

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. \(g=\\{(8,6),(9,6),(3,4),(-4,4)\\}\)

Graph each exponential function. $$ y=4^{x} $$

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

Solve each equation. Give an exact solution and a four-decimal-place approximation. $$ 9^{x}=5 $$

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

Practice using the exponential growth formula by completing the table below. Round final amounts to the nearest whole. $$ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text { Original } \\ \text { Amount } \end{array} & \begin{array}{c} \text { Growth } \\ \text { Rate per Year } \end{array} & \begin{array}{c} \text { Number } \\ \text { of Years, } \boldsymbol{x} \end{array} & \begin{array}{c} \text { Final Amount after } \\ \boldsymbol{x} \text { Years of Growth } \end{array} \\ \hline 2000 & 11 \% & 41 & \\ \hline \end{array} $$

Use a calculator to approximate each logarithm to four decimal places. $$ \log 2.31 $$

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

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. \(h=\\{(10,10)\\}\)

Graph each exponential function. $$ y=1+2^{x} $$

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

Solve each equation. Give an exact solution and a four-decimal-place approximation. $$ 3^{x}=11 $$

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

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

Use a calculator to approximate each logarithm to four decimal places. $$ \log 4.86 $$

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

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. \(r=\\{(1,2),(3,4),(5,6),(6,7)\\}\)

Graph each exponential function. $$ y=3^{x}-1 $$

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

Solve each equation. Give an exact solution and a four-decimal-place approximation. $$ 3^{2 x}=3.8 $$

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

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

Use a calculator to approximate each logarithm to four decimal places. $$ \ln 2 $$

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

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. \(f=\\{(11,12),(4,3),(3,4),(6,6)\\}\)

Graph each exponential function. $$ y=\left(\frac{1}{4}\right)^{x} $$

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

Solve each equation. Give an exact solution and a four-decimal-place approximation. $$ 5^{3 x}=5.6 $$

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

Practice using the exponential growth formula by completing the table below. Round final amounts to the nearest whole. $$ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text { Original } \\ \text { Amount } \end{array} & \begin{array}{c} \text { Growth } \\ \text { Rate per Year } \end{array} & \begin{array}{c} \text { Number } \\ \text { of Years, } \boldsymbol{x} \end{array} & \begin{array}{c} \text { Final Amount after } \\ \boldsymbol{x} \text { Years of Growth } \end{array} \\ \hline 29 & 61 \% & 12 & \\ \hline \end{array} $$

Use a calculator to approximate each logarithm to four decimal places. $$ \ln 3 $$

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

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. \(f=\\{(-1,-1),(1,1),(0,2),(2,0)\\}\)

Graph each exponential function. $$ y=\left(\frac{1}{5}\right)^{x} $$

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

Solve each equation. Give an exact solution and a four-decimal-place approximation. $$ e^{6 x}=5 $$

Write each as an exponential equation. $$ \log _{e} x=4 $$