What is the limit of (a^x - 1)/x as x approaches 0?

[wiz0r]

Homework Statement

lim x->0 ( (a^x - 1)/x )

Homework Equations

NA

The Attempt at a Solution

The professor told me that the answer to that limit is log(a), but why? I don't understand; can someone explain why?

 

[gb7nash]

Do you know l'hopital's rule?

 

[wiz0r]

Do you know l'hopital's rule?

Yeah, I just figured it out. Take the derivative of both the numerator and the denominator and then it's easy from there...

Is there any way to do it without having to use L'Hospital's?

 

[gb7nash]

You could take the maclaurin series of a^x and plug it in for a^x. Once you do this, stuff cancels out and you'll obtain the same answer.