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lim(xto0)(loge(1+x))/(3^x-1) is equal to...

`lim_(xto0)(log_e(1+x))/(3^x-1)` is equal to

A

`log_(e)3`

B

0

C

1

D

`log_(e)e`

Text Solution

Verified by Experts

The correct Answer is:
D
`lim_(xto0)(log_e(1+x))/(3^x-1)=lim_(xto0)((1)/(1+x))/(3^xlog3)` (using L'Hospital's rule)
`=(1)/(log3)=log_(3)e` .
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