Question 18
The domain of the function $$
\tiny f(x)=\log_{\frac{1}{2}}\!\left(\log_4\!\left(\log_{\frac{1}{4}}\!\left(\log_{16}\!\left(\log_{\frac{1}{16}}x\right)\right)\right)\right)
$$ is an interval of length $\dfrac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. What is $m+n?$
\tiny f(x)=\log_{\frac{1}{2}}\!\left(\log_4\!\left(\log_{\frac{1}{4}}\!\left(\log_{16}\!\left(\log_{\frac{1}{16}}x\right)\right)\right)\right)
$$ is an interval of length $\dfrac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. What is $m+n?$