A value of `C` for which the conclusion of mean value theorem bolds for the function `f(x)=glo_e x` on the interval `[1,3]` is `1/2(log)_e3` (b) `(log)_3e` `(log)_e3` (d) `2(log)_3e`

Options

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

Answer

A

Explanation

Given `f(x)=log_(e) ximpliesf'(x)=1/x`
Using Mean Value theorem,
`f'(c)=(f(3)-f(1))/(3-1)implies1/c=(log_(e)3-log_(e)1)/(3-1)`
`impliesc=2/(log_(e)3)=2log_(3)e`