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Math Help - i need some help simplifying this

  1. #1
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    i need some help simplifying this

    (e^log7 - e^-log7)/(e^log7 + e^-log7)

    the answer is supposed to be 24/25, but i have no idea where to begin simplifying this (find tanh (log7))
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  2. #2
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    Quote Originally Posted by twostep08 View Post
    (e^log7 - e^-log7)/(e^log7 + e^-log7)

    the answer is supposed to be 24/25, but i have no idea where to begin simplifying this (find tanh (log7))
    e^{\log{7}} = 7

    e^{-\log{7}} = \frac{1}{7}

    \frac{7 - \frac{1}{7}}{7 + \frac{1}{7}} = \frac{49-1}{49+1} = \frac{48}{50} = \frac{24}{25}<br />
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    ooh.ok.. i dont remember that-what property of logs is that?
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  4. #4
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    Quote Originally Posted by twostep08 View Post
    ooh.ok.. i dont remember that-what property of logs is that?
    b^{\log_b{x}} = x
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  5. #5
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    And that is, basically, the definition of "logarithm".
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