# 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 ->  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

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 Click here to see ALL problems on logarithm 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 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 :)Answer by dabanfield(803)   (Show Source): You can put this solution on YOUR website!Hi, I have a question about writing a series of logs as a single log. The problem I have is: Rewrite the expression 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)