Answer
The statement is false.
To make it true, replace "$e^{2}=x+3$" with "$10^{2}=x+3$".
Work Step by Step
The logarithm (written without a base) is the common logarithm, and its base is 10.
By definition of logarithms ( $ y=\log_{b}x \Leftrightarrow x=b^{y}$),
$\log(x+3)=2$ means $10^{2}=x+3.$