Answer
True.
Work Step by Step
$x \log 10^{x} = x^{2}$
$x \log 10^{x} =x^{2}$
$\log (10^{x})^{x}=x^{2}$
$\log (10^{x^{2}}) =x^{2}$
$x^{2} = x^{2}$
True
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