91Ó°ÊÓ

Use a graphing calculator to solve each equation. Give solutions to the nearest hundredth. $$2^{-x}=\log x$$

Find the \(p H\) for each substance with the given hydronium ion \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) concentration. Sodium hydroxide, \(3.2 \times 10^{-14}\)

For each function that is one-to-one, write an equation for the inverse function of \(y=f(x)\) in the form \(y=f^{-1}(x),\) and then graph \(f\) and \(f^{-1}\) on the same axes. Give the domain and range of \(f\) and \(f^{-1} .\) If the function is not one-to-one, say so. $$y=\frac{1}{x}$$

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\log x=\sqrt{\log x}$$

Use a graphing calculator to solve each equation. Give solutions to the nearest hundredth. $$e^{x}=x^{2}$$

Find the hydronium ion \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) concentration for each substance with the given \(p H\). Soda pop, 2.7

Find the hydronium ion \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) concentration for each substance with the given \(p H\). Wine, 3.4

For each function that is one-to-one, write an equation for the inverse function of \(y=f(x)\) in the form \(y=f^{-1}(x),\) and then graph \(f\) and \(f^{-1}\) on the same axes. Give the domain and range of \(f\) and \(f^{-1} .\) If the function is not one-to-one, say so. $$y=\frac{4}{x}$$

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\ln (\ln x)=0$$

Use a graphing calculator to solve each equation. Give solutions to the nearest hundredth. $$e^{3 x}=x^{3}+4$$