How can I rewrite expression to get log out of exponent

Question

I have the expression $2^{\sqrt{\log(n)}}$, but that's nasty to work with. I watched a few video on logarithms https://www.youtube.com/watch?v=ZIwmZ9m0byI , but none of it seems to cover how I might break the log out?
What are the steps to breaking this apart into something a little more workable?

Answer 1

I think that there are not algebraic manipulation to simplify it.

You can change the base as follow

$$2^{\sqrt{\log n}}=e^{\sqrt{\log n}\cdot \log 2}$$

Answer 2

Perhaps it would be helpful if you set the expression equal to another variable. I've assumed you're using log of base 10, but it will also be similar in another base.

Given: $y = 2^{\sqrt{log_{10}(n)}}$.

This can be rewritten as:

$log_2(y) = \sqrt{log_{10}(n)}$

$(log_2(y))^2 = log_{10}(n)$

$10^{({log_2(y)})^2} = n$