How do you expand #log ((x^3 sqrt (x+1))/(x-2)^2)#?

1 Answer

Answer:

Break down the term into smaller parts, then clean up to get #3logx+(1/2)log(x+1)-2log(x-2)#

Explanation:

Let's start with the original:

#log((x^3sqrt(x+1))/(x-2)^2)#

Right now we have, in essence, 3 log terms - the #x^3# and the square root multiplying each other, and the square term dividing into the numerator. We can break these apart like so:

#logx^3+logsqrt(x+1)-log(x-2)^2#

I'm going to rewrite this to show the square root as an exponent of #1/2#

#logx^3+log(x+1)^(1/2)-log(x-2)^2#

We can now move the exponents to the space in front of the log sign, like this:

#3logx+(1/2)log(x+1)-2log(x-2)#