Question

Simplify log (x2-y2)- log (x-y)=

Answer 1

Using the law of logarithm.  LogA - LogB =  Log(A/B)

log(x²-y²) - log(x-y) = log((x²-y²)/(x-y))

Note by difference of two squares, (x²-y²) = (x-y)(x+y)

Simplifying (x²-y²)/(x-y) = (x-y)(x+y)/(x-y) = (x+y)

Therefore log(x²-y²) - log(x-y) = log((x²-y²)/(x-y)) = log((x-y)(x+y)/(x-y)) = log(x+y)

Answer 2

Remember:
log A - log B=log (A/B)
(a²-b²)=(a+b)(a-b).

Therefore

log (x²-y²)-log(x-y)=log[(x²-y²)/(x-y)]= log[(x+y)(x-y)  / (x-y)]=log (x+y)

Answer: log (x²-y²)-log(x-y)=log (x+y)