Find the value of $x$ if $x^{2} {log}_{10} x = 20$

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Solution

We have,

$x^{2} {log}_{10} x = 20$

${log}_{10} x^{x^{2}} = 20 \dots (n {log}_{a} b = {log}_{a} b^{n})$

We know that, ${log}_{a} b = c ⟹ b = a^{c}$

$x^{x^{2}} = 10^{20}$

Hence, this is the answer.

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