Question 303346
Hi, I have a question about writing a series of logs as a single log. The problem I have is: Rewrite the expression {{{3logx-5log(x^2+1)+2log(x-1)}}}as a single logarithm logA. Then the function A=_____?

I have figured out that 3logx can be rewritten as log(x^3) and 5log(x^2+1)is the same as log(x^2+1)^5, but that's all.

Thank you :)

Good start. We also know that 2log(x-1) = log(x-1)^2.  So now we have:

log(x^3) - log(x^2+1)^5 + log(x-1)^2

Changing the order of the terms and using the laws log x + log y = log x*y and log x - log y = log(x/y) we have:

log (x^3) + log(x-1)^2 - log(x^2+1) =

log ((x^3*(x-1)^2) - log(x^2+1) =

log(x^3*(x-1)^2)/(x^2+1))=
log(x^3*(x^2-2x+1)/(x^2+1))=
log(x^5-2x^4+x^3)/(x^2+1)