91Ó°ÊÓ

Solve the equation. First express your answer in terms of natural logarithms (for instance, \(x=(2+\ln 5) /(\ln 3)) .\) Then use a calculator to find an approximation for the answer. $$3^{x}=5$$

Translate the given logarithmic statement into an equivalent exponential statement. $$\ln 3=1.0986$$

Solve the equation. First express your answer in terms of natural logarithms (for instance, \(x=(2+\ln 5) /(\ln 3)) .\) Then use a calculator to find an approximation for the answer. $$2^{x}=9$$

Sketch a complete graph of the function. $$h(x)=2^{-x^{2}}$$

Compute the ratios of successive entries in the table to determine whether or not an exponential model is appropriate for the data. $$\begin{array}{|l|l|l|l|l|l|l|} \hline x & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline y & 3 & 15.2 & 76.9 & 389.2 & 1975.5 & 9975.8 \\ \hline \end{array}$$

In Exercises \(11-16,\) let \(u=\ln x\) and \(v=\ln y .\) Write the given expression in terms of u and v. For example, $$\ln x^{3} y=\ln x^{3}+\ln y=3 \ln x+\ln y=3 u+v$$ $$\ln \left(x^{2} y^{5}\right)$$

Solve the equation. First express your answer in terms of natural logarithms (for instance, \(x=(2+\ln 5) /(\ln 3)) .\) Then use a calculator to find an approximation for the answer. $$2^{x}=3^{x-1}$$

Compute and simplify. $$x^{1 / 2}\left(x^{2 / 3}-x^{4 / 3}\right)$$

List the transformations needed to transform the graph of \(h(x)=2^{x}\) into the graph of the given function. $$f(x)=2^{x}-5$$

Translate the given logarithmic statement into an equivalent exponential statement. $$\ln .01=-4.6052$$