solve $\log_3^2(x)-\log_2(x)=2$

Question

The solution for the equation $\log_3^2(x)-\log_3(x)=2$ is

a) $s=\{2,-1\}$; b) $s=\{6,-3\}$; c) $s=\{9, 1/3 \}$; d) $s=\{27, 1/9 \}$; e) $s=\{ 1/6 ,12\}$

It was given in a test at school and I could not solve. I put on wolfram and the answer is not on the options. Link

Answer 1

$\left(\frac{\log(x)}{\log(3)}\right)^2-\left(\frac{\log(x)}{\log(2)}\right)=2$
setting $t=\log(x)$ we get a quadratic equation.

Answer 2

From the given options, I guess that you want to solve the following for $x$ : $$(\log_3(x))^2-\log_\color{red}{3}(x)=2.$$ Let $t=\log_3(x)$. Then, we have $$t^2-t-2=0\iff (t-2)(t+1)=0\iff t=2,-1\iff x=3^2,3^{-1}.$$