Answer
$\ln 3$
Work Step by Step
Substitute into the relevant formula:
${\rm sech}^{-1}(\displaystyle \frac{3}{5})=\ln(\frac{1+\sqrt{1-(\frac{3}{5})^{2}}}{(\frac{3}{5})})$
$=\displaystyle \ln(\frac{5(1+\sqrt{16/25}}{3})$
$=\displaystyle \ln(\frac{5(1+\frac{4}{5})}{3})$
$=\displaystyle \ln(\frac{5+4}{3})$
$=\ln 3$
