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Logarithm help

  1. Dec 6, 2006 #1
    I have a question I need to do which I'm stuck on:

    find a

    log[base 2](log[base 3]a) = 2

    How would I do that? And sorry about the crude representation of the base, but I'm not sure how to do a small 2 or 3 on the computer.

    Edit: oh damn, wrong forum. I guess it has to be moved to the appropriate one for homework questions.
    Last edited: Dec 6, 2006
  2. jcsd
  3. Dec 6, 2006 #2
    What have you tried so far? What is the definition of a logarithm?
  4. Dec 7, 2006 #3
    suggest you think about the inverse of logs of an integer base and how easily they can be worked out
  5. Dec 7, 2006 #4

    Gib Z

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    Ok well. log[base a] x = y then a^y= x, by definition.

    Then in this case, 2^2 = log[base 3] a
    log[base3]a = 4

    Indentity- log[base x] y = (ln y)/(ln x) Hopefully uve learned this.

    ln a = 4 ln 3

    make both sides the exponents of e.
    a= e^(4 ln3 )

    Therefore, a = 81.
  6. Dec 7, 2006 #5
    no need for e or your identity, just use your 1st line defn again
  7. Dec 8, 2006 #6

    Gib Z

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    Homework Helper

    o yea that should have been obvious, my bad
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