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

Sep 11, 2015

x=1, ${10}^{\sqrt{3}} , {10}^{-} \sqrt{3}$

#### Explanation:

$\log \left({x}^{3}\right) = 3 \log x$

$3 \log x = {\left(\log x\right)}^{3}$
${\left(\log x\right)}^{3} - 3 \log x = 0$

$\log x \left({\left(\log x\right)}^{2} - 3\right)$=0

logx=0, ${\left(\log x\right)}^{2} - 3 = 0$

log x=0 means x=1 and ${\left(\log x\right)}^{2} - 3 = 0$ would mean $\log x = \pm \sqrt{3}$, or $x = {10}^{\sqrt{3}} , {10}^{-} \sqrt{3}$