91Ó°ÊÓ

Write the exponential equation in logarithmic form. For example, the logarithmic form of \(e^{2}=7.3890 . . .\) is \(\ln 7.3890 . . .=2.\) $$\sqrt[3]{e}=1.3956 . . . $$

Solve the exponential equation algebraically. Round your result to three decimal places. Use a graphing utility to verify your answer. $$e^{x}=e^{x^{2}-2}$$

Use the Leading Coefficient Test to determine the right-hand and left-hand behavior of the graph of the polynomial function. $$f(x)=2 x^{3}-3 x^{2}+x-1$$

You build an annuity by investing \(P\) dollars every month at interest rate \(r,\) compounded monthly. Find the amount \(A\) accrued after \(n\) months using the formula. \(A=P\left[\frac{(1+r / 12)^{n}-1}{r / 12}\right],\) where \(r\) is in decimal form. $$P=\mathrm{S} 25, r=0.12, n=48 \mathrm{months}$$

Write the exponential equation in logarithmic form. For example, the logarithmic form of \(e^{2}=7.3890 . . .\) is \(\ln 7.3890 . . .=2.\) $$\frac{1}{e^{4}}=0.0183. . . $$

Solve the exponential equation algebraically. Round your result to three decimal places. Use a graphing utility to verify your answer. $$e^{2 x}=e^{x^{2}-8}$$

Use the properties of logarithms to condense the expression.$$\frac{5}{2} \log _{7}(z-4)$$.

Use the Leading Coefficient Test to determine the right-hand and left-hand behavior of the graph of the polynomial function. $$f(x)=5-x^{2}-4 x^{4}$$

You build an annuity by investing \(P\) dollars every month at interest rate \(r,\) compounded monthly. Find the amount \(A\) accrued after \(n\) months using the formula. \(A=P\left[\frac{(1+r / 12)^{n}-1}{r / 12}\right],\) where \(r\) is in decimal form. $$P=\$ 100, r=0.09, n=60 \text { months }$$

You build an annuity by investing \(P\) dollars every month at interest rate \(r,\) compounded monthly. Find the amount \(A\) accrued after \(n\) months using the formula. \(A=P\left[\frac{(1+r / 12)^{n}-1}{r / 12}\right],\) where \(r\) is in decimal form. $$P=S 200, r=0.06, n=72 \text { months }$$