91Ó°ÊÓ

Simplify each complex fraction. $$ \frac{2+\frac{1}{x^{2}-1}}{1+\frac{1}{x-1}} $$

A population growing continuously at an annual rate \(r\) will triple in a time \(t\) given by the formula \(t=\frac{\ln 3}{r} .\) How long will it take the population of a town to triple if it is growing at the rate of \(12 \%\) per year?

Use a calculator to solve each equation. Round answers to four decimal places. See Example \(6 .\) $$ \log x=-1.71 $$

Use a graphing calculator to solve each equation. If an answer is not exact, round to the nearest tenth. See Using Your Calculator: Solving Exponential Equations Graphically or Solving Logarithmic Equations Graphically. $$ 2^{x+1}=7 $$

Use the change-of-base formula to find logarithm to four decimal places. \(\log _{1 / 3} 3\)

Use the change-of-base formula to find logarithm to four decimal places. \(\log _{1 / 2} 6\)

Use a calculator to solve each equation. Round answers to four decimal places. See Example \(6 .\) $$ \log x=1.4023 $$

Use a graphing calculator to solve each equation. If an answer is not exact, round to the nearest tenth. See Using Your Calculator: Solving Exponential Equations Graphically or Solving Logarithmic Equations Graphically. $$ 3^{x}-10=3^{-x} $$

Use a graphing calculator to solve each equation. If an answer is not exact, round to the nearest tenth. See Using Your Calculator: Solving Exponential Equations Graphically or Solving Logarithmic Equations Graphically. $$ \log x+\log (x-15)=2 $$

Use the change-of-base formula to find logarithm to four decimal places. \(\log _{3} 8\)