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Logarithmic properties

  1. Jan 23, 2006 #1
    sorry this should go under the " Homework, Coursework, & Textbook Questions" forum. please delete. i will repost.

    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.
     
    Last edited: Jan 23, 2006
  2. jcsd
  3. Jan 23, 2006 #2

    mathman

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    Gold Member

    You must be reading it wrong. Let x=(log base c of a). Then your equation reads x^b=bx, which in general is wrong.

    A correct expression is:

    (log base c of a^b)=b(log base c of a)

    It looks close to what you wrote, so it may be what was meant.
     
  4. Jan 23, 2006 #3

    HallsofIvy

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    Staff Emeritus
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    As mathman said, what you have: (log base c of a)^b = b(log base c of a), more simply written as
    [tex]\left(log_c a\right)^b= b log_c a[/tex]
    is not true.

    Yes, you are reading it wrong. What is true is that
    [tex]log_c\left(a^b\right)= b log_c(a)[/tex]

    How you would prove that depends on exactly which definition of [itex]log_c[/itex] you are using.
     
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