I am having trouble solving this log.
Simply:
25^ log5(xy) + log ( xg * (root)y over (root) x)
My simplification is:
(xy)^2 + log (x^3/4 y^1/2 g /1)
So, you need to simplify:
$\displaystyle \displaystyle 25^{\log_5(xy)} + \log\left(xg \sqrt{\dfrac{y}{\sqrt{x}}\right)\ ?$
Your answer is correct.
You may want to split up the logarithm to the sum of logarithms, depending upon what's meant by 'simplify'.