Chapter 10

Solve each of the equations. $$ 10^{x}=0.0001 $$

Solve each logarithmic equation and express irrational solutions in lowest radical form. $$ \log x+\log (x+21)=2 $$

Use your calculator to find each natural logarithm. Express answers to four decimal places. \(\ln 5\)

Evaluate each logarithmic expression. \(\log _{2} 16\)

Verify that the two given functions are inverses of each other. $$ f(x)=-\frac{1}{2} x+\frac{5}{6} \text { and } g(x)=-2 x+\frac{5}{3} $$

Solve each of the equations. $$ \left(2^{x+1}\right)\left(2^{x}\right)=64 $$

Solve each logarithmic equation and express irrational solutions in lowest radical form. $$ \log x+\log (x+3)=1 $$

Use your calculator to find each natural logarithm. Express answers to four decimal places. \(\ln 18\)

Evaluate each logarithmic expression. \(\log _{3} 9\)

Verify that the two given functions are inverses of each other. $$ f(x)=x^{3}+1 \text { and } g(x)=\sqrt[3]{x-1} $$

Solve each of the equations. $$ \left(2^{2 x-1}\right)\left(2^{x+2}\right)=32 \quad\left\\{\frac{4}{3}\right\\} $$

Solve each logarithmic equation and express irrational solutions in lowest radical form. $$ \log (3 x-1)=1+\log (5 x-2) $$

Use your calculator to find each natural logarithm. Express answers to four decimal places. \(\ln 32.6\)

Evaluate each logarithmic expression. \(\log _{3} 81\)

Verify that the two given functions are inverses of each other. $$ \begin{aligned} &f(x)=\frac{1}{x-1} \quad \text { for } x>1 \quad \text { and } \\ &g(x)=\frac{x+1}{x} \quad \text { for } x>0 \end{aligned} $$

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. \$ 15,000 \text { for } 10 \text { years at } 7.75 \% \quad \$ 32,558.88

Solve each of the equations. $$ (27)\left(3^{x}\right)=9^{x} $$ \(\\{3\\}\)

Solve each logarithmic equation and express irrational solutions in lowest radical form. $$ \log (2 x-1)-\log (x-3)=1 $$

Use your calculator to find each natural logarithm. Express answers to four decimal places. \(\ln 79.5\)

Evaluate each logarithmic expression. \(\log _{2} 512\)

Verify that the two given functions are inverses of each other. $$ \begin{aligned} &f(x)=x^{2}+2 \quad \text { for } x \geq 0 \text { and } \\ &g(x)=\sqrt{x-2} \text { for } x \geq 2 \end{aligned} $$

What rate of interest, to the nearest tenth of a percent, compounded annually is needed for an investment of \(\$ 200\) to grow to \(\$ 350\) in 5 years? \(11.8 \%\)

Solve each of the equations. $$ \left(3^{x}\right)\left(3^{5 x}\right)=81 $$ \(\left\\{\frac{2}{3}\right\\}\)

Solve each logarithmic equation and express irrational solutions in lowest radical form. $$ \log (x+1)=\log 3-\log (2 x-1) $$

Use your calculator to find each natural logarithm. Express answers to four decimal places. \(\ln 430\)

Evaluate each logarithmic expression. \(\log _{6} 216\)

Verify that the two given functions are inverses of each other. $$ \begin{aligned} &f(x)=\sqrt{2 x-4} \text { for } x \geq 2 \text { and } \\ &g(x)=\frac{x^{2}+4}{2} \text { for } x \geq 0 \end{aligned} $$

What rate of interest, to the nearest tenth of a percent, compounded quarterly is needed for an investment of \(\$ 1500\) to grow to \(\$ 2700\) in 10 years? \(\quad 5.9 \%\)

Solve each of the equations. $$ \left(4^{x}\right)\left(16^{\frac{3 x-1}{x}}\right)=8 \quad\left\\{\frac{1}{2}\right\\} $$

Solve each logarithmic equation and express irrational solutions in lowest radical form. $$ \log (x-2)=1-\log (x+3) $$

Use your calculator to find each natural logarithm. Express answers to four decimal places. \(\ln 371.8\)

Evaluate each logarithmic expression. \(\log _{4} 256\)

Verify that the two given functions are inverses of each other. \(f(x)=x^{2}-4\) for \(x \geq 0\) and $$ g(x)=\sqrt{x+4} \text { for } x \geq-4 $$

Find the effective yield, to the nearest tenth of a percent, of an investment at \(7.5 \%\) compounded monthly. \(7.8 \%\)

Solve each logarithmic equation and express irrational solutions in lowest radical form. $$ \log (x+2)-\log (2 x+1)=\log x $$

Use your calculator to find each natural logarithm. Express answers to four decimal places. \(\ln 0.46\)

Evaluate each logarithmic expression. \(\log _{7} \sqrt{7}\)

Determine whether \(f\) and \(g\) are inverse functions. $$ f(x)=3 x \text { and } g(x)=-\frac{1}{3} x $$

Graph each of the exponential functions. $$ f(x)=3^{x} $$

Solve each logarithmic equation and express irrational solutions in lowest radical form. $$ \log (x+1)-\log (x+2)=\log \frac{1}{x} $$

Use your calculator to find each natural logarithm. Express answers to four decimal places. \(\ln 0.524\)

Evaluate each logarithmic expression. \(\log _{2} \sqrt[3]{2}\)

Determine whether \(f\) and \(g\) are inverse functions. $$ f(x)=\frac{3}{4} x-2 \text { and } g(x)=\frac{4}{3} x+\frac{8}{3} $$

What investment yields the greater return: \(7 \%\) compounded monthly or \(6.85 \%\) compounded continuously? \(\quad 7 \%\) compounded monthly

Graph each of the exponential functions. $$ f(x)=4^{x} $$

Solve each logarithmic equation and express irrational solutions in lowest radical form. $$ \ln (2 t+5)=\ln 3+\ln (t-1) $$

Use your calculator to find each natural logarithm. Express answers to four decimal places. \(\ln 0.0314\)

Evaluate each logarithmic expression. \(\log _{10} 1\)

Determine whether \(f\) and \(g\) are inverse functions. $$ f(x)=x^{3} \text { and } g(x)=\sqrt[3]{x} $$

What investment yields the greater return: \(8.25 \%\) compounded quarterly or \(8.3 \%\) compounded semiannually? \(\quad 8.25 \%\) compounded quarterly