Question:$log_{4}(log_{2}(log_{5}(625)))$
I started solving from inside of the question.
I got $4$ then I took it as exponent for log base $2$. I got $2$ then following the same method I got $2$ as the final solution but in the textbook, they have given it as $1/2$. I don't get why it should be in reciprocal when it wasn't negative.
From the inside... $$ \log_4\Big(\log_2\big(\log_5(625)\big)\Big) = \log_4\Big(\log_2\big(4\big)\Big) = \log_4\Big(2\Big) =\frac{1}{2} $$ The last one is because $2^2=4$ and $2 = 4^{1/2}$.