Answer
$$x= \ln \frac{3}{7} $$
Work Step by Step
Since
\begin{align*}
10\left(1+e^{-x}\right)^{-1}&=3\\
1+e^{-x}&= \frac{10}{3}\\
e^{-x}&= \frac{7}{3},\ \ \ \ \text{Take }\ \ln \ \ \text{for both sides }\\
\ln e^{-x}&=\ln \frac{7}{3}\\
-x&=\ln \frac{7}{3}\\
x&= \ln\left( \frac{7}{3}\right)^{-1}
\end{align*}
Then $$x= \ln \frac{3}{7} $$
