simplify
log (xy/z^2)
log^5square root a^4/b^2
powers of logs aren't very common. Do you mean log base 5 for the second one?
Using the properties of logs,
log (xy/z^2) = logx + logy - 2logz
but I'm not sure that's any simpler
log√(a^4/b^2) = log(a^2/b) = 2loga - logb
Not sure what to do with the 5.
If you meant log√(a^4/b^2)^5
then that is log(a^2/b)^5 = log(a^10/b^5) = 10loga-5logb