What is the solution?

Question

Given that log(xy^3)baseb = m and log(x^3.y^2) base b = p

Find log(√(xy)) base b in term of m and p.

The answer is (m+2p)/14 note that all above equation had log as a "base b" pls show working

Answer 1

log(xy^3) + 2log(x^3y^2) = log(x^7y^7)= (m+2p)
log(xy) = 1/7 log(x^7y^7) = 1/7 (m+2p)
log(√(xy)) = 1/2 log(xy) = 1/14(m+2p)