Question

`log (a^2-b^2)` can also be written as what? (look at choices below)

A) `loga^2-logb^2`

B) log `a^2/b^2`

C) log `(a+b)/(a-b)`

D) `2*loga-2*logb`

E) `log (a+b)+log(a-b)`

Please explain step by step! I don't understand how to approach this problem.

Answer 1

E

Explanation:

`a^2-b^2=(a+b)(a-b)` special products

And a multiplication within a `log` may be written as the sum of the logs of the factors: `log(X*Y)=logX+logY`

So this goes to:

`log(a^2-b^2)=log((a+b)(a-b))=log(a+b)+log(a-b)`