<s>[INST] Solving Logarithm Equation Solve for x:$$x^2(\log_{10} x)^5 = 100$$ 
Here's what I've tried:
$(\log_{10} x)^5 = A \\ \log_{ \log x} A= 5 = \frac{\log_{10} A}{\log_{10} \log x}$
Not sure how to continue
 [/INST] $$x^2(\log_{10}x)^{5}=10^2$$
$$x^{\frac{2}{5}}\log_{10}x=10^{\frac{2}{5}}$$
$$\log_{10}x^{x^\frac{2}{5}}=\log_{10}10^{10^\frac{2}{5}}$$
$$x^{x^\frac{2}{5}}=10^{10^\frac{2}{5}}$$
so the $$x=10$$
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