Find the value of log₃(1+1/3) + log(1+1/4) + log₃ (1+1/4) + ......+log₃(1+1/80)
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17
We have to find the value of log₃(1+1/3) + log(1+1/4) + log₃ (1+1/5) + ......+log₃(1+1/80)
solution : log₃(1+1/3) + log₃(1+1/4) + log₃ (1+1/5) + ......+log₃(1+1/80)
= log₃(4/3) + log₃(5/4) + log₃(6/5) + ..... + log₃(81/80)
using concept, logA + logB = log(AB)
= log₃(4/3 × 5/4 × 6/5 × ........ × 81/80)
= log₃(81/3)
= log₃ (27)
= log₃(3³)
= 3
Therefore the value of log₃(1+1/3) + log₃(1+1/4) + log₃ (1+1/5) + ......+log₃(1+1/80) = 3
Answered by
3
log 4/3*5/4*..81/80 =log 81/3 = log 27 = log 3³ = 3
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