91Ó°ÊÓ

Evaluate the logarithms exactly (if possible). $$\log 10^{-2}$$

Write each expression as a single logarithm. $$3 \log _{b} x-\log _{b} y$$

Solve the exponential equations. Make sure to isolate the base to a power first. Round our answers to three decimal places. $$\frac{28}{10^{x}+3}=4$$

Graph the exponential function using transformations. State the \(y\) -intercept, two additional points, the domain, the range, and the horizontal asymptote. $$f(x)=5^{x}-2$$

Write each expression as a single logarithm. $$\frac{1}{2} \log _{b} x+\frac{2}{3} \log _{b} y$$

Diana just graduated from medical school owing \(\$ 80,000\) in student loans. The annual interest rate is \(9 \%\) a. Approximately how many years will it take to pay off her student loan if she makes a monthly payment of \(\$ 750 ?\) b. Approximately how many years will it take to pay off her loan if she makes a monthly payment of \(\$ 1,000 ?\)

Evaluate the logarithms exactly (if possible). $$\log _{1 / 4} 4096$$

Graph the exponential function using transformations. State the \(y\) -intercept, two additional points, the domain, the range, and the horizontal asymptote. $$f(x)=e^{x+1}-4$$

Solve the logarithmic equations exactly. $$\log _{3}(2 x+1)=4$$

Graph the exponential function using transformations. State the \(y\) -intercept, two additional points, the domain, the range, and the horizontal asymptote. $$f(x)=e^{x-1}+2$$