# How do you simplify Ln(1-e^-x)?

$\ln \left(1 - {e}^{-} x\right) = \ln \left(1 - \frac{1}{e} ^ x\right) = \ln \left(\frac{{e}^{x} - 1}{e} ^ x\right)$
From here, use $\ln \left(\frac{a}{b}\right) = \ln \left(a\right) - \ln \left(b\right)$ and $\ln \left({e}^{x}\right) = x$:
=ln(e^x-1)-ln(e^x)=color(blue)(ln(e^x-1)-x