1. Limited time only! Sign up for a free 30min personal 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!

Do you know this property of the logarithm?

  1. Apr 29, 2012 #1
    Playing around with logarithms I found an interesting property that "log b^n(a^n) = log b(a)". Then I tried to find some kind of proof that this is right and not only a coincidence. Ι made a gereral formula for any value of both n's (α and β) so that "log b^β(a^α) = x". Therefore "a^α = b^(β*x)" ; "a = b^(β*x/α)" ; "log b(a) = β*x/α" ; "x = (α/β)*log b(a)". And therefore "log b^β(a^α) = (α/β)*log b(a)".
     
  2. jcsd
  3. Apr 29, 2012 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    It's unclear what that notation is supposed to mean.

    Can you write out what "log b^n(a^n)" means in words? Or perhaps master the forums LaTex: https://www.physicsforums.com/showthread.php?t=546968
     
  4. Apr 29, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I think you mean "[itex]log_{b^n}(a^n)= log_b(a)[/itex]". That is, that the logarithm, base [itex]b^n[/itex], of [itex]a^n[/itex] is the same as the logarithm, base b, of a. (Of course, a and b must be positive.)

    If [itex]y= log_{b^n}(a^n)[/itex] then [itex]a^n= (b^n)^y= b^{ny}= (b^y)^n[/itex]. Can you complete it now?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Do you know this property of the logarithm?
  1. Logarithmic properties (Replies: 2)

Loading...