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Inverse of a Function

If 6x6 =623, ...

Question

If $(6 x)^{6} = 6^{2^{3}}$ , then $x =$

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Solution

$(6 x)^{6} = 6^{2^{3}}$
$\Rightarrow 6^{6} \times x^{6} = 6^{8}$
$\Rightarrow 6^{6} \times x^{6} = 6^{8}$
$\Rightarrow x^{6} = \frac{6^{8}}{6^{6}}$
$\Rightarrow x^{6} = 6^{8 - 6}$
$\Rightarrow x^{6} = 6^{2}$
$\Rightarrow x = (6^{2})^{\frac{1}{6}}$
$\Rightarrow x = 6^{\frac{1}{3}}$
Hence, the required result is $6^{\frac{1}{3}}$ .

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