2. Solve the equation $\log _{3}\left(\log _{2} x+12\right)+2=4$ and write the solution as a fraction.
2. First, we solve $\log _{3}\left(\log _{2} x+12\right)=2$. Considering the definition of the logarithm, we write $3^{2}=\log _{2} x+12$. We rearrange the equation and get $\log _{2} x=-3$. Solving $2^{-3}=x$. The solution is $x=\frac{1}{8}$.

Solving the equation $\log _{3}\left(\log _{2} x+12\right)=2 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

![](https://cdn.mathpix.com/cropped/2024_06_07_cd02ddf507985fa73630g-09.jpg?height=57&width=1642&top_left_y=2539&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_cd02ddf507985fa73630g-09.jpg?height=57&width=1639&top_left_y=2587&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_cd02ddf507985fa73630g-09.jpg?height=54&width=1636&top_left_y=2640&top_left_x=207)$\qquad$