Solve log_b(xy): Express in terms of p, q

[footprints]

\text{Given that } log_b(x^3y)=p \text{ and } log_b(\frac{y}{x^2}) = q \text{ express } log_b(xy) \text{ in terms of p and q.}
\text{ This is what I've done. }
log_b(x^3y)=p----(1)
log_b(\frac{y}{x^2})=q ----(2)
1 - 2
5log_bx=p-q
\text{ I'm stuck here. What do I do next? }

 

[primarygun]

Find log x and log y in terms of p and q first
then split log(xy)

 

[footprints]

Find log x and log y in terms of p and q first

How do I do that?Could you show me the steps?

 

[dextercioby]

How do I do that?Could you show me the steps?

b^{p}=x^{3}y (1);b^{q}=xy^{-2} (2)
(1)=>b^{2p}=x^{6}y^{2} (3)
(2)*(3)=> x^{7}=b^{2p+q} (4) => log_{b}x=...

Did u see a pattern??

 

[footprints]

Nope. I don't see a pattern. But I figured how to do it. Thanks for help.