91Ó°ÊÓ

Find the exact value of the logarithmic expression without using a calculator. (If this is not possible, state the reason.) $$\ln e^{2}+\ln e^{5}$$

Find the domain, \(x\) -intercept, and vertical asymptote of the logarithmic function and sketch its graph. $$f(x)=-\log _{6}(x+2)$$

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=3 e^{x+4}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$5^{-t / 2}=0.20$$

Find the exponential model \(y=a e^{b x}\) that fits the points shown in the graph or table. $$ \begin{array}{|l|l|l|} \hline x & 0 & 4 \\ \hline y & 5 & 1 \\ \hline \end{array} $$

Find the exact value of the logarithmic expression without using a calculator. (If this is not possible, state the reason.) $$2 \ln e^{6}-\ln e^{5}$$

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=2 e^{-0.5 x}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$4^{-3 t}=0.10$$

Find the exponential model \(y=a e^{b x}\) that fits the points shown in the graph or table. $$ \begin{array}{|l|l|l|} \hline x & 0 & 3 \\ \hline y & 1 & \frac{1}{4} \\ \hline \end{array} $$

Find the domain, \(x\) -intercept, and vertical asymptote of the logarithmic function and sketch its graph. $$y=\log _{5}(x-1)+4$$