x raised to the power of x raised to the power of logarithm base 3 x

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Have a question that has me a little stumped. I know that this equation:$$x^\left(log_3x + x^\left(log_3x\right)\right) \neq 162$$

Simplifies to: $$x^\left(log_3x\right) \neq 81$$

My question is how exactly did they come to the second equation. I know from there it simplifies to: $$(3^\left(log_3x\right))^\left(log_3x\right) \neq 3^4$$

And then: $$(log_4x)^2 \neq 4$$