log_e (e^2 x^(lnx) )=log_e (x^3 ) faind x=?


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Question Number 169798 by mathlove last updated on 09/May/22

${l o g}_{e} (e^{2} x^{l n x}) = {l o g}_{e} (x^{3})$ $f a i n d x = ?$
Commented by cortano1 last updated on 09/May/22
$⇒2+(ln x)^2 = 3 ln x ⇒(ln x)^2 −3 ln x+2 = 0 ⇒ { ((ln x=2⇒x=e^2 )),((ln x=1⇒x= e)) :}$
$\Rightarrow 2 + {(\ln x)}^{2} = 3 \ln x$ $\Rightarrow {(\ln x)}^{2} - 3 \ln x + 2 = 0$ $\Rightarrow {\begin{cases} \ln x = 2 \Rightarrow x = e^{2} \\ \ln x = 1 \Rightarrow x = e \end{cases}$
Commented by mathlove last updated on 09/May/22

$t h a n k s$
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