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Exponential function in terms of logarithms

  1. Jul 16, 2007 #1
    1. The problem statement, all variables and given/known data
    Express [tex]b^{x}[/tex] as a function of logarithms.

    2. Relevant equations
    There are a couple of equations in the attempted solution. I can't say if they are actually relevant

    3. The attempt at a solution

    I've investigated the property
    [tex]y = log_{b}(b^{y}),[/tex]
    and also
    [tex]log_{b}(y) = \frac{log_{k}(y)}{log_{k}(b)}[/tex]

    This hasn't help me any.
  2. jcsd
  3. Jul 16, 2007 #2
    I got it. It's

    [tex]b^{x} = e^{x ln(b)} = b + \frac{x ln(b)}{1!}+ \frac{(x ln(b))^{2}}{2!}+ \frac{(x ln(b))^{3}}{3!}+ \frac{(x ln(b))^{4}}{4!}+...[/tex]
    Last edited: Jul 16, 2007
  4. Jul 17, 2007 #3
    Never mind, my mistake.
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