Question

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

Short answer

The solution set of$x=\left\{\frac{1}{4}\right\}$

Step-by-step solution

Step 1. Given information 

An equation,${\log }_{x}64=-3$

Step 2. Required to find 

Solve the given equation to find x.

Step 3. Solving the equation

Given, ${\log }_{x}64=-3$

role="math" localid="1646573803791" $\Rightarrow x^{-3}=64$

role="math" localid="1646573910655" $\Rightarrow x={64}^{-\frac{1}{3}}$

$\Rightarrow x=\frac{1}{{64}^{{\displaystyle \frac{1}{3}}}}$

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