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 (1) `2(log)_3e` (2) `1/2""(log)_e3` (3) `(log)_3e` (4) `(log)_e3`

Options

A. `2 log_(3) e`
B. `(1)/(2) log_(e) 3`
C. `log_(3)e`
D. `log_(e) 3`

Explanation

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`