91Ó°ÊÓ

Use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places.

${\log }_{\mathrm{Ï€}}\sqrt{2}$

In Problems 71– 86, use the given functionf to:

(a) Find the domain of f.

(b) Graph f.

(c) From the graph, determine the range and any asymptotes of f.

(d) Find $f^{-1}$, the inverse of f.

(e) Find the domain and the range of $f^{-1}$.

(f) Graph $f^{-1}$.

$f\left(x\right)=\frac{1}{2}\log x-5$

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:

${\log }_{9}x+3{\log }_{3}x=14$

The domain of a one-to-one functionf is $[0,∞)$, and its range is$[5,∞)$. State the domain and the range of $f^{-1}$.

Solve given equation and verify your result using graphing utility.

$e^{3x}=e^{2-x}$

In Problems 71– 86, use the given functionf to:

(a) Find the domain off.

(b) Graphf.

(c) From the graph, determine the range and any asymptotes off.

(d) Find $f^{-1}$, the inverse off.

(e) Find the domain and the range of $f^{-1}$.

(f) Graph $f^{-1}$.

$f\left(x\right)=\frac{1}{2}\log \left(2x\right)$

Graph each function using a graphing utility and the Change-of-Base Formula.

$y={\log }_{4}x$

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places :

${\left(\sqrt[3]{2}\right)}^{2-x}=2^{x^2}$

The domain of a one-to-one functiong is$(-∞,0)$ , and its range is$[0,∞)$. State the domain and the range of$g^{-1}$ .

Solve given equation and verify your result using graphing utility.

$e^{x^2}=e^{3x}.\frac{1}{e^2}$