loga xy^3=9; loga x^2y=8

Question

Find value of loga (xy)^(1/2)

Answer 1

logx+3logy=9
2logx+logy=8
logx=a
logy=b
a+3b=9
2a+b=8
solve above equations
b=2 and a=3
1/2(a+b)=1/2(2+3)
1/2(logx+logy)=5/2
log(xy)^1/2=5/2