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Differentiate: ln(x) = yln(a)

  1. Dec 25, 2011 #1
    1. The problem statement, all variables and given/known data
    Given that ln(x) = y ln(a)
    find
    dy/dx



    2. Relevant equations



    3. The attempt at a solution

    So
    y = ln(x) / ln(a)
    thus we use the quotient rule
    ln(x) --> 1/x
    ln(a) --> 1/a

    Denominator = [ln(a)]2

    So the differentiated equation is

    ln(a)/x - ln(x)/a
    -------------------
    [ln(a)]2

    How would I continue this
    The answer is
    d/dx = 1/(x ln(a))
     
  2. jcsd
  3. Dec 25, 2011 #2

    vela

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    When you differentiate, you differentiate with respect to some variable, in this case, x. Here the quantity a is a constant. Try redoing your calculation with that in mind.
     
  4. Dec 25, 2011 #3
    d/dx of ln(x) / ln(a)
    d/dx of ln(x) * 1/ln(a)
    LETS SAY 1/ln(a) = k
    thus
    d/dx of k ln(x) equals
    k/x
    this is the same as
    1/xln(a)
    right?
     
  5. Dec 25, 2011 #4

    vela

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    Yup!
     
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