Simplify the following equation log5 1 1 5 log5 1 1 6 log5 1 1 7 hellip log5 1 1 624 ........

Mathematics (NDA) Logarithm

Simplify the following equation log₅(1+1/5)+log₅(1+1/6) +log₅(1 +1/7)….log₅(1+1/624) ?

log₅(1+1/5)+log₅(1+1/6) +log₅(1 +1/7)………….log₅(1+1/624)

=log₅(6/5)+log₅(7/6)+ log₅(8/7)……………………log₅(625/624)

=log₅(6/5 × 7/6 × 8/7 × 9/8 ………625/624)

=log₅625/5

=log₅ 125

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