#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.

1 Answer
May 12, 2018

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)#