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

Question

Brycen Chase

Mathematics

31 August, 23:15

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

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Answers (2)

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Maliyah Butler · 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)

Dale · Answer 2

Remember:

log A - log B=log (A/B)

(a ²-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)