How do you solve $log x^3=(log x)^3$ ?

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I know there are 3 solutions, but I don't know the steps taken to solve it.

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Answer 1 · 2017-07-17T01:50:18

$logx^3=(logx)^3$

$=>logx^3=(logx)^3$

$=>3logx=(logx)^3$

let $logx=y$

then the equation becomes

$y^3-3y=0$

$=>y(y^2-3)=0$

When $y=0$

$=>logx=0=log1$

$=>x=1$

when

$y^2-3=0$

$=>y=pmsqrt3$

$=>logx=pmsqrt3$

$=>x=e^(pmsqrt3)$