Answer
$x=\dfrac{1-\ln12}{4}\approx-0.371227$
Work Step by Step
$8+e^{1-4x}=20$
First, let's solve for $e^{1-4x}$:
$e^{1-4x}=20-8$
$e^{1-4x}=12$
Apply $\ln$ to both sides of the equation:
$\ln e^{1-4x}=\ln12$
The exponent $1-4x$ can be taken down to multiply in front of its respective $\ln$:
$(1-4x)\ln e=\ln12$
Since $\ln e=1$, the equation becomes:
$1-4x=\ln12$
Solve for $x$:
$4x=1-\ln12$
$x=\dfrac{1-\ln12}{4}\approx-0.371227$