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Thread: logs as exponents

  1. #1
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    logs as exponents

    Hi;
    I know that x^logx3 = 3 but what if the bases are not the same i.e. x^logy3 = ? for example, How do I solve these ones?

    Thanks.
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  2. #2
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    Re: logs as exponents

    In general any logarithm, to any base, has the property that log(a^b)= blog(a). In particular log(x^logy(3))= log_y(3)log(x). That second logarithm can be to any base.
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  3. #3
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    Re: logs as exponents

    $$x^{\log_y z} = z^{\log_y x}$$

    This is fairly easy to prove but does not simplify the problem much.
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