Question

In the following exercises, convert each logarithmic equation to exponential form.

$5={\log }_{x}32$

Short answer

$x^5=32$

Step-by-step solution

Step 1. Given Information

$5={\log }_{x}32$

Step 2. Calculation 

The logarithmic form $y={\log }_{a}x$

is equivalent to exponential form$x=a^y$.

Comparing $5={\log }_{x}32$

with standard form $y={\log }_{a}x$, you have

$$\begin{gathered} y=5, \\ a=x, \\ x=32 \end{gathered}$$

Convert logarithmic form in exponential form as shown below:

$$\begin{gathered} x=a^y \\ 32=x^5 \\ {x}^5=32 \end{gathered}$$

Therefore, if$5={\log }_{x}32$

role="math" localid="1644943653226" $\text{then}{x}^5=32.$