# Find x in log &#x2061;<!-- ⁡ --> x 2 </msup> = ( log &#x20

Find $x$ in $\mathrm{log}{x}^{2}=\left(\mathrm{log}x{\right)}^{2}$
I couldn't find x.
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Bruno Dixon
$\mathrm{log}{x}^{2}=\left(\mathrm{log}x{\right)}^{2}\phantom{\rule{0ex}{0ex}}2\mathrm{log}x=\left(\mathrm{log}x{\right)}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{log}x\left(\mathrm{log}x-2\right)=0\phantom{\rule{0ex}{0ex}}\mathrm{log}x=0\to x=1\phantom{\rule{0ex}{0ex}}\mathrm{log}x=2\to x={10}^{2}$
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Patatiniuh
Hint: Note that
$\mathrm{log}{x}^{2}=2\mathrm{log}x$
for all $x>0.$ Now use the substitution $u=\mathrm{log}x$ to get
$2u={u}^{2}.$
Solve for $u,$ then solve for $x.$