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Math Help - exponent equation

  1. #1
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    exponent equation

    Hello, I have the following equation:

    5^x = 4^x+1

    I am confident the first two steps are:
    (using common log)

    a) log5^x = log 4^x+1
    b) xlog5 = x+1log 4

    However I can not figure out to finish the problem.

    Can someone please help ?
    Thanks kindly
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  2. #2
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    e^(i*pi)'s Avatar
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    5^x = 4^{x+1}. It's a very important bracket there, as you wrote it +1 is not in the exponent. Also (x+1)\log(4) \neq x+1\log(4)


    Nonetheless you're on the right track: x\log_{10}(5) = x\log_{10}(4) + \log_{10}(4) \implies x\log_{10}(5) - x\log_{10}(4) = \log_{10}(4)


    x is now a factor of both terms on the LHS. Can you finish?


    edit: if the answer has \log_{10}(2) in then recall \log(4) = 2\log(2)
    Last edited by e^(i*pi); March 28th 2011 at 02:47 PM. Reason: see post
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