How do you simplify lne^lnx?

Apr 3, 2018

$\ln {e}^{\ln} x = \ln x$

Explanation:

As $\ln {a}^{b} = b \cdot \ln a$,

$\ln {e}^{\ln} x = \ln x \cdot \ln e$

but as base in $\ln x$ is $e$, $\ln e = 1$

hence $\ln {e}^{\ln} x = \ln x$

Apr 3, 2018

$\ln x$
$\ln {e}^{\ln} x$=$\ln x \cdot \ln e$
$\ln e = 1$
$\therefore$$\ln {e}^{\ln} x = \ln x$