1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about Log Laws

  1. Apr 8, 2008 #1
    I don't know how I managed to forget this one, but I did somehow...

    If there's something like:

    e^lnx, why is that equal to just x?

    and same goes for sokmething like:

    8^log8x which is just equal to x.

    I'm just wondering how, algebraically, one could show this to be true.
     
  2. jcsd
  3. Apr 8, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You generally DEFINE ln(x) to be the inverse function of e^x. Or vice versa depending on which you define first. So you don't show it algebraically, it largely a matter of definition.
     
  4. Apr 8, 2008 #3
    well, by definition of log we have

    [tex]log_a(x)=b<=> a^b=x[/tex]

    Now lets substitute [tex] b=log_a(x)[/tex] in
    [tex]a^b=x[/tex] So:

    [tex]a^{log_a(x)}=x[/tex]

    Or, since [tex]f(x)=a^x[/tex] and [tex]g(x)=log_ax[/tex] are inverse functions, so it means that they cancel each other out. That is

    [tex]fg(x)=f(g(x))=x=>a^{log_ax}=x[/tex] and also

    [tex] g(f(x))=log_a(a^x)=x[/tex]

    Edit: Dick was faster!
     
  5. Apr 8, 2008 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are slow because you write more. Doesn't mean you think slower. I appreciate the TeX though.
     
    Last edited: Apr 8, 2008
  6. Apr 8, 2008 #5
    Oh I see now! Thanks so much for your help Dick and sutupidmath!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Question about Log Laws
  1. Question about log (Replies: 1)

  2. Log Law Question (Replies: 3)

  3. Laws of logs (Replies: 4)

Loading...