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Math Help - Exponential using two different bases.

  1. #1
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    Exponential using two different bases.

    8x-1 = 9x+3

    Solve for x.

    My attempt:
    I'm guessing since they're both equal, if I multiply them it will just be the same as squaring one side.

    We have (8x-1)(9x+3)=72x^2+2x-3

    ANNNNND I don't know what to do next. I tried equating x2+2x-3 = 2 since 72x^2+2x-3 = a2 where a is the base. Solving for x2+2x-5=0, I got:


    x = \ -1\pm\sqrt{6}

    How do I solve this? I need to find the base.
    Last edited by RPSGCC733; October 16th 2012 at 02:34 AM.
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  2. #2
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    Re: Exponential using two different bases.

    Hey RPSGCC733.

    Recall that you can calculate the log in any base by log_b(x) = log_c(x)/log_c(b) where log_c(x) is the logarithm in base c.

    This means that you can calculate log_9(x) in terms of log_8(x) and vice versa.
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