# How do you simplify ln(lne^(e^10))?

$\ln \left(\ln {e}^{{e}^{10}}\right) = 10$
As functions of Real numbers, $\ln \left(x\right)$ and ${e}^{x}$ are inverses of one another.
$\ln \left(\ln {e}^{{e}^{10}}\right) = \ln \left({e}^{10}\right) = 10$