Chapter 5, Problem 37RE

In Problems 35-45, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility.

${\log }_{x}64\text{ = }-3$

To determine

To find: Irrational solutions in exact form in the given function.

Answer to Problem 37RE

$x=\frac{1}{4}$

Explanation of Solution

Given:

${\text{log}}_{x}64=-3$

Calculation:

${\text{log}}_{x}64=-3$

${\left(x^{-3}\right)}^{\frac{-1}{3}}={\left(64\right)}^{\frac{-1}{3}}$

$x={\left(64\right)}^{\frac{-1}{3}}$

$x=\frac{1}{\sqrt[3]{64}}=\frac{1}{4}$