91Ó°ÊÓ

Find the \(p H\) for each substance with the given hydronium ion \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) concentration. Limes, \(1.6 \times 10^{-2}\)

Solve each equation in part (a) analyrically. Support your answer with a calculator graph. Then use the graph to solve the associated inequalities in parts (b) and (c). (a) \(3^{2-x}=9\) (b) \(3^{2-x}>9\) (c) \(3^{2-x}<9\)

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\log _{2}(2 x)+\log _{2}(x+2)=\log _{2} 16$$

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. $$y=-x^{3}-2$$

Find the \(p H\) for each substance with the given hydronium ion \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) concentration. Crackers, \(3.9 \times 10^{-9}\)

Solve each equation in part (a) analyrically. Support your answer with a calculator graph. Then use the graph to solve the associated inequalities in parts (b) and (c). (a) \(27^{4 x}=9^{x+1}\) (b) \(27^{4 x}>9^{x+1}\) (c) \(27^{4 x}<9^{x+1}\)

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\ln e^{x}-2 \ln e=\ln e^{4}$$

Use a graphing calculator to solve each equation. Give solutions to the nearest hundredth. $$\log x=\frac{1}{2} x-1$$

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\log _{2}\left(\log _{2} x\right)=1$$

Solve each equation in part (a) analyrically. Support your answer with a calculator graph. Then use the graph to solve the associated inequalities in parts (b) and (c). (a) \(32^{x}=16^{1-x}\) (b) \(32^{x}>16^{1-x}\) (c) \(32^{x}<16^{1-x}\)