I just don't understand why the log is squared $$\log^2x-3\log x=\log x^2-4$$
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7$(\log(x))^2$ is often represented as $\log^2(x)$. Notice that it is a quadratic equation in terms of $\log(x)$ – DatBoi Sep 16 '20 at 05:49
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See also: What does $\log^{2}{x}$ mean? – Martin Sleziak Sep 16 '20 at 08:22
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HINT
The notation stands for: $\log^2 x=(\log x)(\log x)$.
Then use that $\log x^2=2\log x$ and let $\log x=t$ to obtain a quadratic.
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Let $log x=y$, then $$log^2 x-3log x=log x^2-4$$ $$y^2-3y=2y-4$$ $$y^2-5y+4=0$$ $$(y-1)(y-4)=0$$ $y=1$ or $y=4$ $$log x=1$$ or $$log x=4$$
Hence $x=10 $ or $x=10000$
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