Answer
$x=3^{1/3}=\sqrt[3]3$
Work Step by Step
We have to solve the logarithmic equation:
$$\log_{x}(\log_{3}27)=3.$$
Rewrite it in exponential form:
$$\log_{a}b=c\Rightarrow b=a^c$$
$$\log_{3}27=x^3$$
But $\log_{3}27=3$ because $3^3=27$, therefore we have:
$$3=x^3$$
$$x=3^{1/3}=\sqrt[3]3$$
Check if the solution is valid:
$$\log_{\sqrt[3]3}(\log_3 27)=\log_{\sqrt[3]3}\log_3 3^3=\log_{\sqrt[3]3} 3=\log_{\sqrt[3]3}(\sqrt[3]3)^3=3\checkmark$$
