91Ó°ÊÓ

Find the hydronium ion \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) concentration for each substance with the given \(p H\) Beer, 4.8

For each function that is one-to-one, write an equation for the inverse function 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. $$y=\frac{2}{x+3}$$

Use a graphing calculator to solve each equation. Give solutions to the nearest hundredth. $$2^{-x}=\log _{10} x$$

Concept Check If \(f(x)=a^{x}\) and \(f(3)=27,\) find each value of \(f(x)\) (a) \(f(1)\) (b) \(f(-1)\) (c) \(f(2)\) (d) \(f(0)\)

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

Give an exponential function in the form \(f(x)=a^{x}\) whose graph contains the given point. \((3,8)\)

Find the hydronium ion \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) concentration for each substance with the given \(p H\) Drinking water, 6.5

For each function that is one-to-one, write an equation for the inverse function 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. $$y=\frac{3}{x-4}$$

Use the properties of logarithms to rewrite each logarithm if possible. Assume that all variables represent positive real numbers. $$\log _{3} \frac{2}{5}$$

A student told a friend, "You must reject any negative solution of an equation involving logarithms." Is this correct? Write an explanation of your answer.