Chapter 11

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ 3^{x}=32 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 7.24\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 2^{7}=128 $$

Assuming that the rate of inflation is \(4 \%\) per year, the equation \(P=P_{0}(1.04)^{t}\) yields the predicted price \(P\), in \(t\) years, of an item that presently costs \(P_{0}\). Find the predicted price of each of the following items for the indicated years ahead. (a) $$\$ 1.38$$ can of soup in 3 years (b) $$\$ 3.43$$ container of cocoa mix in 5 years (c) $$\$ 1.99$$ jar of coffee creamer in 4 years (d) $$\$ 1.54$$ can of beans and bacon in 10 years (e) $$\$ 18,000$$ car in 5 years (nearest dollar) (f) $$\$ 180,000$$ house in 8 years (nearest dollar) (g) $$\$ 500 \mathrm{TV}$$ set in 7 years (nearest dollar)

For Problems \(1-34\), solve each equation. $$ 3^{x}=27 $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ 2^{x}=40 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 2.05\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 3^{3}=27 $$

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 (b) $$\$ 22,000$$ car after 2 years (c) $$\$ 27,000$$ car after 5 years (d) $$\$ 40,000$$ car after 3 years

For Problems \(1-34\), solve each equation. $$ 2^{2 x}=16 $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ 4^{x}=21 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 52.23\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 5^{3}=125 $$

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. (Objective 1) $$\$ 200$$ for 6 years at \(6 \%\) compounded annually

For Problems \(1-34\), solve each equation. $$ 2^{2 x}=16 $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ 5^{x}=73 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 825.8\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 2^{6}=64 $$

For Problems \(1-34\), solve each equation. $$ 3^{2 x}=81 $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ 3^{x-2}=11 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 3214.1\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 10^{3}=1000 $$

$$\$ 500$$ for 7 years at \(4 \%\) compounded semiannually

For Problems \(1-34\), solve each equation. $$ \left(\frac{1}{4}\right)^{x}=\frac{1}{256} $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ 2^{x+1}=7 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 14,189\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 10^{1}=10 $$

$$\$ 750$$ for 8 years at \(4 \%\) compounded semiannually

For Problems \(1-34\), solve each equation. $$ \left(\frac{1}{2}\right)^{x}=\frac{1}{128} $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ 5^{3 x+1}=9 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 0.729\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 2^{-2}=\left(\frac{1}{4}\right) $$

$$\$ 800$$ for 9 years at \(5 \%\) compounded quarterly

For Problems \(1-34\), solve each equation. $$ 5^{x+2}=125 $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ 7^{2 x-1}=35 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 0.04376\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 3^{-4}=\left(\frac{1}{81}\right) $$

$$\$ 1200$$ for 10 years at \(4 \%\) compounded quarterly

For Problems \(1-34\), solve each equation. $$ 4^{x-3}=16 $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ e^{x}=5.4 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 0.00034\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 10^{-1}=0.1 $$

$$\$ 1500$$ for 5 years at \(8 \%\) compounded monthly

For Problems \(1-34\), solve each equation. $$ 3^{-x}=\frac{1}{243} $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ e^{x}=45 $$

For Problems \(1-10\), use a calculator to find each common logarithm. Express answers to four decimal places. \(\log 0.000069\)

For Problems \(1-10\), write each of the following in logarithmic form. For example, \(2^{3}=8\) becomes \(\log _{2} 8=3\) in logarithmic form. $$ 10^{-2}=0.01 $$

$$\$ 2000$$ for 10 years at \(3 \%\) compounded monthly

For Problems \(1-34\), solve each equation. $$ 5^{-x}=\frac{1}{25} $$

For Problems \(1-14\), solve each exponential equation and express solutions to the nearest hundredth. $$ e^{x-2}=13.1 $$