91Ó°ÊÓ

Graph functions \(f\) and \(g\) in the same rectangular coordinate system. Select integers from \(-2\) to 2 , inclusive, for \(x\). Then describe how the graph of g is related to the graph of \(f .\) If applicable, use a graphing utility to confirm your hand-drawn graphs. $$f(x)=3^{x} \text { and } g(x)=3 \cdot 3^{x}$$

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(1 .\) Where possible, evaluate logarithmic expressions. $$\log 250+\log 4$$

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(1 .\) Where possible, evaluate logarithmic expressions. $$\ln x+\ln 7$$

Evaluate each expression without using a calculator. $$\log _{5} 5^{7}$$

Use the compound interest formulas, \(A=P\left(1+\frac{r}{n}\right)^{n-1}\) and \(A=P e^{n t},\) to solve Exercises \(39-42 .\) Round answers to the nearest cent. Find the accumulated value of an investment of \(\$ 10,000\) for 5 years at an interest rate of \(5.5 \%\) if the money is a. compounded semiannually; b. compounded monthly; c. compounded continuously.

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$2^{x+1}=5^{x}$$

Evaluate each expression without using a calculator. $$\log _{4} 4^{6}$$

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(1 .\) Where possible, evaluate logarithmic expressions. $$\ln x+\ln 3$$

Use the compound interest formulas, \(A=P\left(1+\frac{r}{n}\right)^{n-1}\) and \(A=P e^{n t},\) to solve Exercises \(39-42 .\) Round answers to the nearest cent. Find the accumulated value of an investment of \(\$ 5000\) for 10 years at an interest rate of \(6.5 \%\) if the money is a. compounded semiannually; b. compounded monthly; c. compounded continuously.

Solve each exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$4^{x+1}=9^{x}$$