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Shouldn't these 2 equations be equal?

  1. May 26, 2012 #1
    1. The problem statement, all variables and given/known data
    I was doing a math problem, where I forgot to simplify e3ln2.


    2. Relevant equations



    3. The attempt at a solution

    Instead of doing e3ln2 = eln(2^3) = eln(8) = 8, I did the following:


    e3ln2 = e3*eln2 = 2e3

    However, 2e3 ≠ 8.

    What happened?
    Mod edit: The OP figured it out.
     
    Last edited by a moderator: May 27, 2012
  2. jcsd
  3. May 27, 2012 #2
    Just in case someone stumbles here with the same problem, my mistake was to assume e3ln2 = e3*eln2.

    That statement is false since e3*eln2 = e3+ln2 ≠ e3ln2.
     
  4. May 27, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Well, lets hope that people who are attempting to solve problems like this will know that [itex]e^{x+ y}= e^xe^y\ne e^{xy}[/itex].
     
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