Condense log x-2 log(x+1)

Question

I need to condense the expression of the logarithm of a single quantity.

Answer 1

You need the following two log identities:

• b log(a) = log(a^b)
• log(a)-log(b) = log(a/b)

 

log(x) - 2 log(x+1)

 

Using the first identity, we get:

 

log(x) - log((x+1)²)

 

Using the second identity we get:

 

log(x/(x+1)²)