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. $$9^{x-1}=8^{x-3}$$

Compute the ratios of successive entries in the table to determine whether or not an exponential model is appropriate for the data. $$\begin{array}{|l|l|l|l|l|l|l|} \hline x & 1 & 3 & 5 & 7 & 9 & 11 \\ \hline y & 3 & 21 & 55 & 105 & 171 & 253 \\ \hline \end{array}$$

In Exercises \(11-16,\) let \(u=\ln x\) and \(v=\ln y .\) Write the given expression in terms of u and v. For example, $$\ln x^{3} y=\ln x^{3}+\ln y=3 \ln x+\ln y=3 u+v$$ $$\ln \left(x^{4} y^{3}\right)$$

Translate the given logarithmic statement into an equivalent exponential statement. $$\ln s=r$$

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

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

List the transformations needed to transform the graph of \(h(x)=2^{x}\) into the graph of the given function. $$k(x)=3\left(2^{x}\right)$$

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

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

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