5. Continuity and Differentiation
normal

The value of $\left[ {\frac{{\log \left( {\frac{x}{e}} \right)}}{{x - \,e}}} \right]\,\forall x\, > \,e$ is equal to (where [.] denotes greatest integer function)

A

$1$

B

$0$

C

$2$

D

does not take unique value

Solution

$\frac{\log x-\log \mathrm{e}}{x-e}=\frac{1}{c} c \in(e, x)(L M V T)$

$\Rightarrow 0<\frac{\log \left(\frac{x}{e}\right]}{x-e}<1$

Standard 12
Mathematics

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