91Ó°ÊÓ

Use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\log \frac{9}{300}$$

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. $$ \begin{array}{l} f(x)=27^{x} \\ g(x)=9 \end{array} $$

Evaluate the function at the indicated value of \(x\) without using a calculator. $$ \begin{array}{cc} \text { Function } & \text { Value } \\ f(x)=\log x & x=10 \end{array} $$

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. $$ \begin{array}{l} f(x)=\log _{3} x \\ g(x)=2 \end{array} $$

Evaluate the function at the indicated value of \(x\) without using a calculator. $$ \begin{array}{cc} \text { Function } & \text { Value } \\ g(x)=\log _{a} x & x=a^{2} \end{array} $$

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

Use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\ln \left(5 e^{6}\right)$$

Use the graph of \(f\) to describe the transformation that yields the graph of \(g\). $$f(x)=0.3^{x}, \quad g(x)=-0.3^{x}+5$$

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. $$ \begin{array}{l} f(x)=\ln (x-4) \\ g(x)=0 \end{array} $$

Evaluate the function at the indicated value of \(x\) without using a calculator. $$ \begin{array}{cc} \text { Function } & \text { Value } \\ g(x)=\log _{b} x & x=b^{-3} \end{array} $$