# Correct one: Solve for x, log_2 (log_3x) = 2?

Jan 18, 2018

I got the same answer as the other answerer, using a different method: $x = 64$

#### Explanation:

Start with ${\log}_{2} \left({\log}_{3} x\right) = 2$

Raise both sides to the power of 2:

${\left({\log}_{2} \left({\log}_{3} x\right)\right)}^{2} = {2}^{2} = 4$

Note that ${\log}_{2} {\left(\text{anything}\right)}^{2}$= $\text{anything}$

That is, ${\log}_{2} {\left(3\right)}^{2} = 3$, ${\log}_{2} {\left(6\right)}^{2} = 6$ and so on.

So then ${\log}_{3} \left(x\right) = 4$

Now raise both sides to the power 3:

${\log}_{3} {\left(x\right)}^{3} = {4}^{3} = 64$

Same as above, ${\log}_{3} {\left(x\right)}^{3} = x$

So $x = 64$.