`lim_(x to 0) (log_(5)(1+x))/(x)` किसके बराबर है ?

Options

A. 1
B. `log_(5)e`
C. `log_(e)5`
D. 5

Answer

B

Explanation

`underset(xrarr0)lim(log_(5)(1+x))/(x)`
`=underset(xrarr0)lim(log_(e)(1+x))/(log_(e)5(x))[:'log_(a)b=(log_(e)b)/(log_(e)a)]`
`=(1)/(log_(e)5)underset(xrarr0)lim log_(e).((1+x))/(x)`
`=(1)/(log_(e)5)[:'underset(xrarr0)lim(log_(e)(1+x))/(x)=1]`
`=log_(5)e[:'log_(a)b=(1)/(log_(b)a)]`