Question

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

$4=\ln \left(x\right)$

Short answer

The exponential form is $e^4=x$.

Step-by-step solution

Step 1. Concept used 

Consider the logarithmic form $4=\ln \left(x\right)$.

The logarithmic form role="math" localid="1645022611896" $y={\log }_a\left(x\right)$is equivalent to exponential form

$a^y=x$.

Step 2. Write in exponential form 

Comparing $4=\ln \left(x\right)$with the standard form,

$y={\log }_a\left(x\right)$we have

$$\begin{gathered} y=4 \\ a=e \\ x=x \end{gathered}$$

So substituting the values in the standard exponential form $a^y=x$ we get

$$\begin{gathered} a^y=x \\ {e}^4=x \end{gathered}$$