# Homework Help: Ln vs. log in Short Calculus book by Serge Lang

1. Apr 12, 2010

### freetofu

1. The problem statement, all variables and given/known data

I've been going through a book called "Short Calculus: The Original Edition of A First Course in Calculus," by Serge Lang. It says, " The derivative of a^x is a^x (log a)." But everything else I look at says the derivative of a^x is a^x (ln a). Since ln a and log a are different numbers, I don't see how both equations could be true. And, in fact, the Lang book never mentions ln at all!

The Lang book was 1st published in 1964 (although this is a 2002 printing). Could that be the explanation?

2. Relevant equations

3. The attempt at a solution

2. Apr 12, 2010

### Dick

If you write log_b(a) you mean log to the base b of a. If you just write log(a) that generally means log_e(a) which is the same as ln(a) as far as I know. What do you think log(a) means? I don't think Lang means log_10(a).

3. Apr 12, 2010

### freetofu

OK, I found it it, you're right. He just briefly mentions it at the end of the section. Confusing if you're new to it. Thanks.