#### Answer

The correct answer is $x = e^{2} - 2$.

#### Work Step by Step

$\ln (x+2) = 2$
$\ln_e (x+2) = 2$
$e^{2} = x + 2$
$e^{2} - 2 = x$
$x = e^{2} - 2$
The student thought that the base of the natural log function is $10$, when it actually is $e$. Therefore he/she was unable to find the correct answer.