91Ó°ÊÓ

Approximate the point of intersection of the graphs of \(f\) and \(g\). Then solve the equation \(f(x)=g(x)\) algebraically to verify your approximation. $$ \begin{array}{l} f(x)=\ln (x-4) \\ g(x)=0 \end{array} $$

Complete the table for the time \(t\) (in years) necessary for \(P\) dollars to triple if interest is compounded annually at rate \(r\). $$ \begin{array}{|l|l|l|l|l|l|l|} \hline r & 2 \% & 4 \% & 6 \% & 8 \% & 10 \% & 12 \% \\ \hline t & & & & & & \\ \hline \end{array} $$

Find the exact value of the logarithmic expression without using a calculator. (If this is not possible, state the reason.) $$\log _{3} 9$$

Use a graphing utility to graph the exponential function. $$y=2^{-x^{2}}$$

Use a calculator to evaluate \(f(x)=\log x\) at the indicated value of \(x\). Round your result to three decimal places. $$x=\frac{7}{8}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$e^{x}=e^{x^{2}-2}$$

Find the exact value of the logarithmic expression without using a calculator. (If this is not possible, state the reason.) $$\log _{5} \frac{1}{125}$$

Use a graphing utility to graph the exponential function. $$y=3^{-|x|}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$e^{2 x}=e^{x^{2}-8}$$

Use a calculator to evaluate \(f(x)=\log x\) at the indicated value of \(x\). Round your result to three decimal places. $$x=\frac{1}{500}$$