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Math Help - Logarthimic proof

  1. #1
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    Logarthimic proof

    i have the following:

    b^h = e^ah

    i have been told to take the log of each side and show that there is a value of a for every h. Can i do the following?:

    ln b^h = ah

    but ln b^h = h ln b


    so lnb^h = h ln b = ah

    cancel h

    ln b^h= lb b = a

    divide through by ln b

    h = a

    ???? doesnt read right to me.......
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by thermalwarrior View Post
    i have the following:

    b^h = e^ah

    i have been told to take the log of each side and show that there is a value of a for every h. Can i do the following?:

    ln b^h = ah

    but ln b^h = h ln b


    so lnb^h = h ln b = ah

    cancel h

    ln b^h= lb b = a

    divide through by ln b

    h = a

    ???? doesnt read right to me.......
    Something is screwy:
    b^h = e^{ah}

    ln(b^h) = ln(e^{ah})

    h \cdot ln(b) = ah

    ln(b) = a

    So a has nothing to do with h...

    -Dan
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  3. #3
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    so is h could just be any value just attached onto the final form?
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  4. #4
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    Quote Originally Posted by thermalwarrior View Post
    so is h could just be any value just attached onto the final form?
    That's correct. You even don't need any logarithms:

    b^h = e^{ah} = \left(e^a \right)^h ~\implies~ b = e^a
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