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

  1. Apr 12, 2010 #1
    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. jcsd
  3. Apr 12, 2010 #2


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    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).
  4. Apr 12, 2010 #3
    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.
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