# Question #9ba25

May 6, 2017

${\left(\log \left(x\right)\right)}^{2} - \log {\left(x\right)}^{2} = 3$

This is a quadratic in $\log \left(x\right)$:

${\left(\log \left(x\right)\right)}^{2} - 2 \log \left(x\right) - 3 = 0$

We can factor it:

$\left(\log \left(x\right) + 1\right) \left(\log \left(x\right) - 3\right) = 0$

$\implies \log \left(x\right) = - 1 , 3$

Then it depends upon what base you are using. Assuming ${\log}_{\textcolor{red}{10}}$

$\implies x = \frac{1}{10} , 1000$