91Ó°ÊÓ

In Exercises \(15-20,\) use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\log _{4} 8$$

Evaluate the function at the indicated value of \(x\) without using a calculator. \(\begin{array}{cl}\text { Function } & \text { Value } \\\\\text { 15. } f(x)=\log _{2} x & x=64\end{array}\)

Determine the time necessary for \(P\) dollars to double when it is invested at interest rate \(r\) compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. $$r=10 \%$$

Evaluate the function at the indicated value of \(x\) without using a calculator. $$f(x)=\log _{25} x \quad x=5$$

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. $$\begin{aligned} &f(x)=\log _{3} x\\\ &g(x)=2 \end{aligned}$$ (GRAPH CANNOT COPY)

In Exercises \(15-20,\) use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\log _{2}\left(4^{2} \cdot 3^{4}\right)$$

Determine the time necessary for \(P\) dollars to double when it is invested at interest rate \(r\) compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. $$r=6.5 \%$$

In Exercises \(15-20,\) use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\log _{5} \frac{1}{250}$$

Function \(\quad\) Value \(\begin{array}{ll}\text { 57. } f(x)=\ln x & x=18.42 \\ \text { 58. } f(x)=3 \ln x & x=0.74\end{array}\) \(\begin{array}{lll}y & f(x)=3 \ln x & x=0.74 \\ \text { 59. } g(x)=8 \ln x & x=0.05\end{array}\) 60\. \(g(x)=-\ln x \quad x=\frac{1}{2}\)

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=\left(\frac{1}{2}\right)^{x}$$