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A value of c for which the conclusion of...

A value of c for which the conclusion of Mean value theorem holds for the function `f(x) = log_(e)x` on the interval [1, 3] is

A

`2 log_(3) e`

B

`(1)/(2) log_(e) 3`

C

`log_(3)e`

D

`log_(e) 3`

Text Solution

Verified by Experts

The correct Answer is:
A
Using Mean value theorem,
`f'(c) = (f(3)-f(1))/(3-1)`
`rArr(1)/(c) = (log_(e)3-log_(e)1)/(2)`
`rArr c = (2)/(log_(e)3) = 2log_(3)e`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 17-MATHEMATICS
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