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

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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)
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