91Ó°ÊÓ

Use a graphing utility to solve each equation. Express your answer rounded to two decimal places. $$ e^{2 x}=x+2 $$

Use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. \(\log _{\pi} e\)

Find the real zeros of $$f(x)=x^{5}-x^{4}-15 x^{3}-21 x^{2}-16 x-20$$ Then write \(f\) in factored form.

Use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. \(\log _{\pi} \sqrt{2}\)

In Problems 79-84, graph each function using a graphing utility and the Change-of-Base Formula. \(y=\log _{4} x\)

The domain of a one-to-one function \(g\) is \([0,15],\) and its range is (0,8) . State the domain and the range of \(g^{-1}\).

For \(f(x)=\frac{2 x^{2}-5 x-4}{x-7},\) find all vertical asymptotes, horizontal asymptotes, and oblique asymptotes, if any.

The function \(f(x)=|x|\) is not one-to-one. Find a suitable restriction on the domain of \(f\) so that the new function that results is one-to-one. Then find the inverse of the new function.

\(f(x)=\log _{3}(x+5)\) and \(g(x)=\log _{3}(x-1)\) (a) Solve \(f(x)=2\). What point is on the graph of \(f ?\) (b) Solve \(g(x)=3\). What point is on the graph of \(g\) ? (c) Solve \(f(x)=g(x)\). Do the graphs of \(f\) and \(g\) intersect? If so, where? (d) Solve \((f+g)(x)=3\). (e) Solve \((f-g)(x)=2\).

The function \(f(x)=x^{4}\) is not one-to-one. Find a suitable restriction on the domain of \(f\) so that the new function that results is one-to-one. Then find the inverse of the new function.