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Question: Answered & Verified by Expert
If ϕx=log8⁡log3⁡x, then ϕ ′ e is equal to
MathematicsDifferentiationJEE Main
Options:
  • A elog⁡8
  • B –elog⁡8
  • C 1elog⁡8
  • D None of these
Solution:
2189 Upvotes Verified Answer
The correct answer is: 1elog⁡8
We have,
ϕx=log8⁡log3⁡x=log8⁡log⁡xlog⁡3
=log8⁡log⁡x-log8⁡log⁡3
=log⁡log⁡xlog⁡8-log8⁡log⁡3
ϕ ′ x = 1 log8 ⋅ 1 logx ⋅ 1 x −0
∴ ϕ ′ e = 1 log8 ⋅ 1 loge ⋅ 1 e = 1 elog8

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