Use the Laws of Logarithms to combine the expression.

Question

1/5log(x + 3)^5 +1/3 [log x^6 − log(x^2 − x − 12)^3]

Answer 1

1/5 log(x+3)^5 = log(x+3)

log(x^6)-log(x^2-x-12)^3
= 3log(x^2/(x^2-x-12)^3)
= log((x^2)/(x^2-x-12))

so, adding those logs, we have

log(x+3) + log((x^2)/(x^2-x-12))
= log(x^2(x+3) / (x+3)(x-4))
= log(x^2/(x-4))