Question

log 1/2 + log 2/3 + log 3/4 + log 4/5 - log 1/5 = 0​

Answer 1

1/2)+log(2/3)+log(3/4)+log(4/5)+log(5/6+log(6/7)....log(98/98)+log(99/100)

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Fact: loga(b) = logc(b)/logc(a)

This is the "Change of Base Law".

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Using that over and over and over agin on you problem

you will see that everything cancels except 

log(1)/log(100)

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= 0/2 = 0

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Cheers,

Stan H.