How do you simplify ${ln e}^{ln x}$ $lne^lnx$ ?

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Answer 1 · 2018-04-03T13:09:18

${ln e}^{ln x} = ln x$ $lne^lnx=lnx$

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

${ln e}^{ln x} = ln x \cdot ln e$ $lne^lnx=lnx*lne$

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

hence ${ln e}^{ln x} = ln x$ $lne^lnx=lnx$

Answer 2 · 2018-04-03T13:19:23

$ln x$ $lnx$

it's known that:
${ln e}^{ln x}$ $lne^lnx$ = $ln x \cdot ln e$ $lnx*lne$
And
$ln e = 1$ $lne=1$
$therefore$ $lne^lnx=lnx$

How do you simplify lne^lnxlnelnxlne^lnx?