# How do you simplify ln sqrt(e^2 + 1) - 1/2 ln (1+ 1/e^2)?

$1$
$\ln \sqrt{{e}^{2} + 1} - \frac{1}{2} \ln \left(1 + \frac{1}{e} ^ 2\right) = \frac{1}{2} \ln \left({e}^{2} + 1\right) - \frac{1}{2} \left(\ln \left({e}^{2} + 1\right) - 2\right)$
$= 1$