SOLUTION: 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. The

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 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. The      Log On


   

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%28x%5E2%2B1%29%2B2log%28x-1%29as 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 :)
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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%28x%5E2%2B1%29%2B2log%28x-1%29as 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)