91Ó°ÊÓ

Use a calculator to find a decimal approximation for each common or natural logarithm. $$\ln 28^{3}$$

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. $$y=3 x-4$$

Solve each equation. Do not use a calculator. $$_{0}^{1-x}=\left(\frac{1}{36}\right)^{2 x} $$

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. $$y=4 x-5$$

Use a calculator to find a decimal approximation for each common or natural logarithm. $$\ln (47 \times 93)$$

Solve each equation. Do not use a calculator. $$\left(\frac{3}{5}\right)^{-x}=\left(\frac{9}{25}\right)^{1-5 x}$$

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) \(2^{x+1}=8\) (b) \(2^{x+1}>8\) (c) \(2^{x+1}<8\)

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\log _{7}(4 x)-\log _{7}(x+3)=\log _{7} x$$

Find the \(p H\) for each substance with the given hydronium ion \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) concentration. Grapefruit, \(6.3 \times 10^{-4}\)

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. $$y=x^{3}+1$$