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I just don't understand why the log is squared $$\log^2x-3\log x=\log x^2-4$$

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    $\begingroup$ $(\log(x))^2$ is often represented as $\log^2(x)$. Notice that it is a quadratic equation in terms of $\log(x)$ $\endgroup$
    – DatBoi
    Sep 16, 2020 at 5:49
  • $\begingroup$ See also: What does $\log^{2}{x}$ mean? $\endgroup$ Sep 16, 2020 at 8:22

2 Answers 2

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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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