Answer
$ln(2+\sqrt 5)\approx1.444$
Work Step by Step
Step 1. Let $u=e^{x}$. Multiply both sides of the equation by $u$ and rearrange to get $u^2-1=4u \longrightarrow u^2-4u-1=0 \longrightarrow u=\frac{4\pm\sqrt {16+4}}{2}=2\pm\sqrt 5$
Step 2. For $e^x=2+\sqrt 5$, we have $x=ln(2+\sqrt 5)\approx1.444$
Step 3. For $e^x=2-\sqrt 5\approx-0.236$, there is no real solution.
Step 4. Check, $x=ln(2+\sqrt 5)\approx1.444$ fits the original equation.
