Question

loga xy^3=9
loga x^2y=8
Find value of loga (xy)^(1/2)

Answer 1

I think we shall make heavy use of these two properties of logs...
\[\Large \log_a(MN)= \log_aM + \log_aN\]
and\[\Large \log_aM^{\color{green}p}=\color{green}p\log_aM\]

Answer 2

mr BEAAN is that you!

Answer 3

A system of linear equations in disguise :3
Or something~~
But the OP is not making his/her presence felt :/