Question

rewrite the following expression as a single logarithm:
3log(x+4)+2log(x-7)-5log(x-2)-log(x^2)

Answer 1

Remember the following 3 rules of logarithms:
1. Added logarithms can be combined to be a single logarithm of a product.
2. Subtracted logarithms can be combined to be a single logarithm of a fraction
3. Coefficients in front of logarithms can be taken as a power of the expression inside the logarithm.

Answer 2

3log(x+4)+2log(x-7)-5log(x-2)-log(x^2)
=log((x+4)^3)+log((x-7)^2)-log((x-2)^5)-log(x^2)
= log(((x+4)^3(x-7)^2)/((x-2)^5*x^2)))