Chapter 10

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 3^{x}=13 $$

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 7.24 $$

Write each exponential statement in logarithmic form. For example, \(2^{5}=32\) becomes \(\log _{2} 32=\) 5 in logarithmic form. (c) \(\left(g^{-1} \circ f^{-1}\right)(x)\) \(\frac{x+7}{6}\) $$ 2^{7}=128 $$

Assuming that the rate of inflation is \(4 \%\) per year, the equation \(P=P_{0}(1.04)^{t}\) yields the predicted price \((P)\) of an item in \(t\) years that presently costs \(P_{0}\). Find the predicted price of each of the following items for the indicated years ahead: (a) \(\$ 0.77\) can of soup in 3 years \(\$ 0.87\) (b) \(\$ 3.43\) container of cocoa mix in 5 years \(\$ 4.17\) (c) \(\$ 1.99\) jar of coffee creamer in 4 years \(\$ 2.33\) (d) \(\$ 1.05\) can of beans and bacon in 10 years \(\$ 1.55\) (e) \(\$ 18,000\) car in 5 years (nearest dollar) \(\$ 21,900\) (f) \(\$ 120,000\) house in 8 years (nearest dollar) \(\$ 164,228\) (g) \(\$ 500 \mathrm{TV}\) set in 7 years (nearest dollar) \(\$ 658\)

Solve each of the equations. $$ 2^{x}=64 $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 2^{x}=21 $$

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 2.05 $$

Suppose it is estimated that the value of a car depreciates \(30 \%\) per year for the first 5 years. The equation \(A=P_{0}(0.7)^{t}\) yields the value \((A)\) of a car after \(t\) years if the original price is \(P_{0}\). Find the value (to the nearest dollar) of each of the following cars after the indicated time: (a) \(\$ 16,500\) car after 4 years \(\$ 3962\) (b) \(\$ 22,000\) car after 2 years \(\$ 10,780\) (c) \(\$ 27,000\) car after 5 years \(\$ 4538\) (d) \(\$ 40,000\) car after 3 years \(\$ 13,720\)

Solve each of the equations. $$ 3^{x}=81 $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 4^{n}=35 $$

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 52.23 $$

Write each exponential statement in logarithmic form. For example, \(2^{5}=32\) becomes \(\log _{2} 32=\) 5 in logarithmic form. (c) \(\left(g^{-1} \circ f^{-1}\right)(x)\) \(\frac{x+7}{6}\) $$ 5^{3}=125 $$

For Problems \(3-14\), 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. \(\$ 200\) for 6 years at \(6 \%\) compounded annually \(\$ 283.70\)

Solve each of the equations. $$ 3^{2 x}=27 \quad\left\\{\frac{3}{2}\right\\} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 5^{n}=75 $$

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 825.8 $$

Write each exponential statement in logarithmic form. For example, \(2^{5}=32\) becomes \(\log _{2} 32=\) 5 in logarithmic form. (c) \(\left(g^{-1} \circ f^{-1}\right)(x)\) \(\frac{x+7}{6}\) $$ 2^{6}=64 $$

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. $$ \$ 250 \text { for } 5 \text { years at } 7 \% \text { compounded annually } $$

Solve each of the equations. $$ 2^{2 x}=16 $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 2^{x}+7=50 $$

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 3214.1 $$

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. \(\$ 500\) for 7 years at \(8 \%\) compounded semiannually \(\$ 865.84\)

Solve each of the equations. $$ \left(\frac{1}{2}\right)^{x}=\frac{1}{128} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 3^{x}-6=25 $$

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 14,189 $$

Solve each of the equations. $$ \left(\frac{1}{4}\right)^{x}=\frac{1}{256} $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 3^{x-2}=11 $$

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 0.729 $$

Write each exponential statement in logarithmic form. For example, \(2^{5}=32\) becomes \(\log _{2} 32=\) 5 in logarithmic form. (c) \(\left(g^{-1} \circ f^{-1}\right)(x)\) \(\frac{x+7}{6}\) $$ 2^{-2}=\frac{1}{4} $$

Determine whether the function \(f\) is one-to-one. $$ f(x)=5 x+4 $$

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. \(\$ 800\) for 9 years at \(9 \%\) compounded quarterly \(\$ 1782.25\)

Solve each of the equations. $$ 3^{-x}=\frac{1}{243} $$

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

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 0.04376 $$

Write each exponential statement in logarithmic form. For example, \(2^{5}=32\) becomes \(\log _{2} 32=\) 5 in logarithmic form. (c) \(\left(g^{-1} \circ f^{-1}\right)(x)\) \(\frac{x+7}{6}\) $$ 3^{-4}=\frac{1}{81} $$

Determine whether the function \(f\) is one-to-one. $$ f(x)=-3 x+4 $$

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. \(\$ 1200\) for 10 years at \(10 \%\) compounded quarterly \(\$ 3222.08\)

Solve each of the equations. $$ 3^{x+1}=9 $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 5^{3 t+1}=9 $$

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 0.00034 $$

Determine whether the function \(f\) is one-to-one. $$ f(x)=x^{3} $$

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. \(\$ 1500\) for 5 years at \(12 \%\) compounded monthly $$ \$ 2725.05 $$

Solve each of the equations. $$ 6^{3 x-1}=36 $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ 7^{2 t-1}=35 $$

Use a calculator to find each common logarithm. Express answers to four decimal places. $$ \log 0.000069 $$

Determine whether the function \(f\) is one-to-one. $$ f(x)=x^{5}+1 $$

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. \(\$ 2000\) for 10 years at \(9 \%\) compounded monthly \(\$ 4902.71\)

Solve each of the equations. $$ 2^{2 x+3}=32 $$

Solve each exponential equation and express approximate solutions to the nearest hundredth. $$ e^{x}=27 $$

Use your calculator to find \(x\) when given \(\log x\). Express answers to five significant digits. $$ \log x=2.6143 $$