What is the simplified form of 2 log (x2 - 1) - log (x + 1) - 2 log (x - 1)?

[nvez]

Hello again..

Homework Statement

I
I have to change this to one term only, the valid answer is: log (x + 1)

The term is: 2 log (x² - 1) - log (x + 1) - 2 log (x - 1)

Homework Equations

Logarithmic laws:

x log n = log n^x
log m - log n = log (m/n)

The Attempt at a Solution

I have tried dividing them but I don't see to be getting anywhere or anywhere close at all at the answer, I also tried factorising but I cannot figure it out, I'm pretty sure that it has some factorization (perfect squares? not sure what they're called in english..)

Thank you in advanced, this forum is a very useful resource!

 

[grief]

So you said you tried dividing. That gives log ( (x²-1)²/((x+1)(x-1)²) ). Now you just need to use the fact that (x²-1)=(x-1)(x+1), and some things will cancel out.

 

[rock.freak667]

Note that x²-1=(x+1)(x-1)

Use some indices and you should get it.

 

[nvez]

The exact thing I needed!

Thank you guys, I can't appreciate this enough.