Answer
$x \approx 3.39$
Work Step by Step
RECALL:
$\ln{x}= y \longrightarrow e^y=x$
Use the rule above to obtain:
$e^{1}=\sqrt{x+4}$
Square both sides of teh equation to obtain:
$e^2=x+4$
Subtract $4$ on both sides of the equation to obtain:
$e^2-4=x$
Use a calculator to obtain:
$x=3.389056099
\\x \approx 3.39$