Question

log5 (1+1/5) + log5 ( 1+1/6)+.......+log5 (1+1/624) =​

Answer 1

Answer:

Required value = 3

Step-by-step explanation:

Now, log₅(1 + 1/5) + log₅(1 + 1/6) + ... + log₅(1 + 1/624)

= log₅(1 + 1/5) + log₅(1 + 1/6) + log₅(1 + 1/7) + log₅(1 + 1/8) + ... + log₅(1 + 1/623) + log₅(1 + 1/624)

= log₅(6/5) + log₅(7/6) + log₅(8/7) + log₅(9/8) + ... + log₅(624/623) + log₅(625/624)

= log₅(6/5 * 7/6 * 8/7 * 9/8 * ... * 624/623 * 625/624)

= log₅(625/5)

= log₅(125)

= log₅(5³)

= 3 log₅(5)

= 3 [ ∵ logₐ(a) = 1 ]

Answer 2

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