Given that x=a^m and y=a^n.Express log^a(3 square root x over ay^2) in terms of m and n.

Answer 1

log (3√x / ay^2)
= log3 + 1/2 logx - loga - 2logy
= log3 + m/2 - 1 - 2n

Don't know whether that 3 belongs there, but there you have it.

If by 3square root you mean cube root, then I'm sure you can make the fix.