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Math Help - Using Log to solve for variable in the exponent

  1. #1
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    Using Log to solve for variable in the exponent

    I need help solving the following:

    c(1+g1)^n = k(1+g2)^n

    where c and k are positive constants and g1 and g2 are growth rates. need to solve for n

    c>k g2>g1

    I should know how to do this but I am having trouble. Thank you
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  2. #2
    A Plied Mathematician
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    I would try this:

    \dfrac{c}{k}=\dfrac{(1+g_{2})^{n}}{(1+g_{1})^{n}}=  \left(\dfrac{1+g_{2}}{1+g_{1}}\right)^{\!\!n}.

    Can you continue?
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  3. #3
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    is this correct then?

    [log(c/k)]/log[(1+g2)/1+g1)] =

    I appreciate the help. Can you refer me to a source that gives basic log rules? I should have learned them in high school math class but I must not have been paying attention during those classes
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  4. #4
    A Plied Mathematician
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    See here for a list of the basic logarithmic identities.

    You don't have an equation in post # 3. So, I would not agree with your result as is.
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  5. #5
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    ok I am sorry,

    [log(c/k)]/log[(1+g2)/1+g1)] = n
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  6. #6
    A Plied Mathematician
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    You just need one more parenthesis in there. Put it like this:

    [log(c/k)]/log[(1+g2)/(1+g1)] = n. Then you have it.
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