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

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Homework Help Overview

The problem involves simplifying a logarithmic expression: 2 log (x² - 1) - log (x + 1) - 2 log (x - 1). Participants are exploring the application of logarithmic laws to combine the terms into a single logarithmic expression.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to simplify the expression by dividing terms and considering factorization, expressing uncertainty about the correct approach. Other participants suggest using known identities and properties of logarithms to facilitate simplification.

Discussion Status

Participants are actively engaging with the problem, providing hints and guidance on how to manipulate the logarithmic terms. There is a sense of collaborative exploration, with some participants confirming the validity of the original poster's attempts and offering additional insights.

Contextual Notes

The original poster indicates a need to arrive at a single term, which may impose constraints on the methods discussed. There is also mention of potential factorization, suggesting that assumptions about the structure of the expression are being examined.

nvez
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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 nx
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!
 
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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.
 
Note that x2-1=(x+1)(x-1)

Use some indices and you should get it.
 
The exact thing I needed!

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

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