Question
Use the Laws of Logarithms to combine the expression.
1/5log(x + 3)^5 +1/3 [log x^6 − log(x^2 − x − 12)^3]
1/5log(x + 3)^5 +1/3 [log x^6 − log(x^2 − x − 12)^3]
Answers
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))
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))
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