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Math Help - simplify natural log times natural log

  1. #1
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    simplify natural log times natural log

    So i have this problem that i am supposed to simplify to a single logarithm or single exponential.

    Log3(5) * Log5(3)

    So far i have
    ln(5/3) * ln(3/5)

    how do i simplify this even more? is there a rule for multiplying two natural logs? thanks!
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  2. #2
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    Are you sure this is correct?

    I get

    \log_3(5) = \frac{\ln(5)}{\ln(3)}

    and

    \log_5(3) = \frac{\ln(3)}{\ln(5)}

    therefore

    \log_3(5) \times \log_5(3) = \frac{\ln(5)}{\ln(3)}\times \frac{\ln(3)}{\ln(5)} = 1
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Are you sure this is correct?

    I get

    \log_3(5) = \frac{\ln(5)}{\ln(3)}

    and

    \log_5(3) = \frac{\ln(3)}{\ln(5)}

    therefore

    \log_3(5) \times \log_5(3) = \frac{\ln(5)}{\ln(3)}\times \frac{\ln(3)}{\ln(5)} = 1

    ohh okay that makes sense. Thanks!
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