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.