ANSWER:
-1
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\log _6\mleft(36^x\mright)=-2[/tex]
Being a logarithmic equation, we will apply properties of logarithms to solve, like this:
[tex]\begin{gathered} 36^x=u \\ \text{ therefore:} \\ \log _6(u)=-2 \\ u=6^{-2} \\ u=\frac{1}{6^2}=\frac{1}{36} \\ \text{ replacing} \\ 36^x=\frac{1}{36} \\ 36^x=36^{-1} \\ x=-1 \end{gathered}[/tex]
The solution set is -1
