Answer
$x=-\ln4\approx-1.386294$
Work Step by Step
$\dfrac{10}{1+e^{-x}}=2$
Take the denominator $1+e^{-x}$ to multiply to the right side of the equation:
$10=2(1+e^{-x})$
$10=2+2e^{-x}$
Now, solve for $e^{-x}$:
$2e^{-x}=10-2$
$2e^{-x}=8$
$e^{-x}=\dfrac{8}{2}$
$e^{-x}=4$
Apply $\ln$ to both sides of the equation:
$\ln e^{-x}=\ln4$
The exponent $-x$ can be taken down to multiply in front of its respective $\ln$:
$-x\ln e=\ln4$
Since $\ln e=1$, the equation becomes:
$-x=\ln4$
Solve for $x$:
$x=-\ln4\approx-1.386294$
