Answer
$x=-\ln\dfrac{23}{2}\approx-2.442347$
Work Step by Step
$\dfrac{50}{1+e^{-x}}=4$
Take the denominator of the left side of the equation to multiply to the right side:
$4(1+e^{-x})=50$
Take the $4$ to divide the right side of the equation:
$1+e^{-x}=\dfrac{50}{4}$
$1+e^{-x}=\dfrac{25}{2}$
Solve for $e^{-x}$:
$e^{-x}=\dfrac{25}{2}-1$
$e^{-x}=\dfrac{23}{2}$
Apply $\ln$ to both sides of the equation:
$\ln e^{-x}=\ln\dfrac{23}{2}$
The exponent $-x$ can be taken down to multiply in front of its respective $\ln$:
$-x\ln e=\ln\dfrac{23}{2}$
Since $\ln e=1$, the equation becomes:
$-x=\ln\dfrac{23}{2}$
Solve for $x$:
$x=-\ln\dfrac{23}{2}\approx-2.442347$
