Answer
$x=\dfrac{\ln19-1}{4}\approx0.486110$
Work Step by Step
$1+e^{4x+1}=20$
First, let's solve for $e^{4x+1}$:
$e^{4x+1}=20-1$
$e^{4x+1}=19$
Apply $\ln$ to both side of the equation:
$\ln e^{4x+1}=\ln19$
The exponent $4x+1$ can be taken down to multiply in front of its respective $\ln$:
$(4x+1)\ln e=\ln19$
Since $\ln e=1$, the equation becomes:
$4x+1=\ln19$
Solve for $x$:
$4x=\ln19-1$
$x=\dfrac{\ln19-1}{4}\approx0.486110$