Answer
The solution set is $x=$ {$\frac{1}{100}, 100$}
Work Step by Step
$$3|\log x|-6=0$$
*Domain: $x\in R, x\gt0$ $$3|\log x|=6$$ $$|\log x|=2$$
As $|X|=A$, either $X=A$ or $X=-A$. Therefore, $$\log x=2$$ or $$\log x=-2$$
* For $\log x=2$ $$\log x=2$$ $$x=10^2=100$$
- Check again: $$3|\log100|-6=3|2|-6=3\times2-6=0$$
That means $x=100$ is a solution to this problem.
* For $\log x=-2$ $$\log x=-2$$ $$x=10^{-2}$$ $$x=\frac{1}{10^2}=\frac{1}{100}$$
- Check again: $$3|\log\frac{1}{100}|-6=3|\log10^{-2}|-6=3|-2|-6=3\times2-6=0$$
$x=\frac{1}{100}$ is also a solution to this problem.
In conclusion, the solution set is $x=$ {$\frac{1}{100}, 100$}
