Question

If a^3 + 3ab(a+b+3)+b^3 = 10ab, show that log (a+b)=1/3(log a + log b). Please show step by step. Thank you!

Answer 1

a^3 + 3ab(a+b+3) + b^3 = 10ab

a^3 + 3a^2b + 3ab^2 + 9ab + b^3 = 10ab
a^3 + 3a^2b + 3ab^2 + b^3 = ab
(a+b)^3 = ab
take log of both sides

log (a+b)^3= log ab
3 log(a+b) = log a + log b
log (a+b) = (1/3)(log a + log b)

Q.E.D.

Answer 2

Thank you!