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Logarithmic properties

  1. Jan 23, 2006 #1
    Okay i did a search for logarithmic properties and logarithms and couldn't seem to find an explanation for how this particular property works.
    (log base c of a ) ^ b = b (log base c of a)
    when i input simple numbers like :
    PHP:
    a=4
    b=3
    c=2
    Log base 2 of 4 obvioussly the answer is 2, but
    2^3 /= (does not equel) 3 x 2.
    i dont' know how to make sense of this discrepency. i imagine i'm just reading it wrong.
     
  2. jcsd
  3. Jan 23, 2006 #2
    hmmm the right formula is [tex]log_c(a)^b=blog_c(a)[/tex]

    edit: heh, im tired =P
     
    Last edited: Jan 23, 2006
  4. Jan 23, 2006 #3
    because [tex](c^a)^b=c^{a*b}[/tex].
     
    Last edited: Jan 23, 2006
  5. Jan 23, 2006 #4

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    Actually the correct formula is:

    [tex]\log_c(a^b) = b\log_c (a)[/tex]

    This can be proven by taking the base c exponential of each side:

    [tex]c^{\log_c(a^b)} = a^b[/tex]

    [tex]c^{b\log_c (a)} = (c^{\log_c (a)})^b= (a)^b[/tex]
     
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