Chapter 10

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{3} 81=4 $$

Determine whether the function \(f\) is one-to-one. $$ f(x)=|x|+1 $$

Use the formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) to find the total amount of money accumulated at the end of the indicated time period for each of the following investments. \(\$ 5000\) for 15 years at \(8.5 \%\) compounded annually \(\$ 16,998.71\)

Solve each of the equations. $$ \left(\frac{3}{4}\right)^{n}=\frac{64}{27} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ e^{x}=86 $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=1.5263 $$

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{2} 256=8 $$

Determine whether the function \(f\) is one-to-one. $$ f(x)=-|x|-2 $$

Use the formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) to find the total amount of money accumulated at the end of the indicated time period for each of the following investments. \(\$ 7500\) for 20 years at \(9.5 \%\) compounded semiannually \(\$ 47,997.93\)

Solve each of the equations. $$ \left(\frac{2}{3}\right)^{n}=\frac{9}{4} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ e^{x-2}=13.1 $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=4.9547 $$

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{4} 64=3 $$

Determine whether the function \(f\) is one-to-one. $$ f(x)=-x^{4} $$

Use the formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) to find the total amount of money accumulated at the end of the indicated time period for each of the following investments. \(\$ 8000\) for 10 years at \(10.5 \%\) compounded quarterly \(\$ 22,553.65\)

Solve each of the equations. $$ 16^{x}=64 \quad\left\\{\frac{3}{2}\right\\} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ e^{x-1}=8.2 $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=3.9335 $$

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{5} 25=2 $$

Determine whether the function \(f\) is one-to-one. $$ f(x)=x^{4}+1 $$

Use the formula \(A=P\left(1+\frac{r}{n}\right)^{n t}\) to find the total amount of money accumulated at the end of the indicated time period for each of the following investments. \(\$ 10,000\) for 25 years at \(9.25 \%\) compounded monthly \(\$ 100,104.82\)

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 3 e^{x}-1=17 $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=1.9006 $$

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{10} 10,000=4 $$

(a) list the domain and range of the function, (b) form the inverse function \(f^{-1}\), and (c) list the domain and range of \(f^{-1}\). $$ f=\\{(1,5),(2,9),(5,21)\\} $$

Solve each of the equations. $$ 27^{4 x}=9^{x+1} \quad\left\\{\frac{1}{5}\right\\} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 2 e^{x}=12.4 $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=0.5517 $$

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{10} 100,000=5 $$

(a) list the domain and range of the function, (b) form the inverse function \(f^{-1}\), and (c) list the domain and range of \(f^{-1}\). $$ f=\\{(1,1),(4,2),(9,3),(16,4)\\} $$

Solve each of the equations. $$ 32^{x}=16^{1-x} \quad\left\\{\frac{4}{9}\right\\} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 5^{2 x+1}=7^{x+3} $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=-1.3148 $$

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{2}\left(\frac{1}{16}\right)=-4 $$

(a) list the domain and range of the function, (b) form the inverse function \(f^{-1}\), and (c) list the domain and range of \(f^{-1}\). $$ f=\\{(0,0),(2,8),(-1,-1),(-2,-8)\\} $$

Solve each of the equations. $$ 9^{4 x-2}=\frac{1}{81} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 3^{x-1}=2^{x+3} $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=-0.1452 $$

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{5}\left(\frac{1}{125}\right)=-3 $$

(a) list the domain and range of the function, (b) form the inverse function \(f^{-1}\), and (c) list the domain and range of \(f^{-1}\). $$ f=\\{(-1,1),(-2,4),(-3,9),(-4,16)\\} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 3^{2 x+1}=2^{3 x+2} $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=-2.1928 $$

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{10} 0.001=-3 $$

Verify that the two given functions are inverses of each other. $$ f(x)=5 x-9 \text { and } g(x)=\frac{x+9}{5} $$

Use the formula \(A=P e^{n}\) to find the total amount of money accumulated at the end of the indicated time period by compounding continuously. \(\$ 2000\) for 15 years at \(10 \%\) \(\$ 8963.38\)

Solve each of the equations. $$ 10^{x}=0.1 \quad\\{-1\\} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 5^{x-1}=2^{2 x+1} $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=-2.6542 $$

Write each logarithmic statement in exponential form. For example, \(\log _{2} 8=3\) becomes \(2^{3}=8\) in exponential form. $$ \log _{10} 0.000001=-6 $$

Verify that the two given functions are inverses of each other. $$ f(x)=-3 x+4 \text { and } g(x)=\frac{4-x}{3} $$