log(x^2 + 3x + 2) - 2log(x+1) ..... write as a single logarithm.

Okay, so the first place to start is to rewrite the term 2log(x+1) as log(x+1)^2 because log contains the property logx^n = n*logx. So the expression now looks like:

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

Another property of log is that logx - logy = log(x/y). So the above can be rewritten as:

log((x^2 + 3x +2)/(x+1)^2)

But x^2 +3 + 2 can be factored into (x+1)(x+2). So you can cancel an (x+1) term from both the numerator and denominator. The final expression should look like:

log((x+2)/(x+1)).

If I'm not mistaken I don't think it can be simplified anymore. I hope this is useful.