The number of solution(s) of the equation ln( | vedclass

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Question

$\ell n(\ell nx) = {\log _x}e \Rightarrow \ell n(\ell nx) = \frac{1}{{\ell nx}}$

Let $\ell n{\rm{x}} = {\rm{t}}$

$\ell n{\rm{t}} = \frac{1}{{\rm

Vedclass · Accepted Answer

$0$

Vedclass · Answer

$\ell n(\ell nx) = {\log _x}e \Rightarrow \ell n(\ell nx) = \frac{1}{{\ell nx}}$

Let $\ell n{m{x}} = {m{t}}$

$\ell n{m{t}} = \frac{1}{{m{t}}}$

it has one solution

$t \in(1, e)$

$\Rightarrow \ell n x<1$ (Reject)

$\because \ell n({\mathop{m nx}
olimits} ) < 0$ but $\log _{x} e>0$

The number of solution$(s)$ of the equation $ln(lnx)$ = $log_xe$ is -

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