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Math Help - removing e,unsure of natural logs

  1. #1
    Member i_zz_y_ill's Avatar
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    removing e,unsure of natural logs

    Not so sure about this! Is it wrong so say

    (-1/3)ln|1-3y| = -1/x + c

    e^(-1/3)ln|1-3y| = e^(-(1/x)+c)

    (-1/3)(1-3y) = Ae^-1/x

    Do I always have to bring the 1/3 to the front like ln|1-3y|^1/3 before removing the e??

    btw how do you get the pi symbol above the toolbar for using lateX (dy/dx) etc?
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by i_zz_y_ill View Post
    Not so sure about this! Is it wrong so say

    (-1/3)ln|1-3y| = -1/x + c

    e^(-1/3)ln|1-3y| = e^(-(1/x)+c)
    That's right
    (-1/3)(1-3y) = Ae^-1/x
    That's wrong
    Do I always have to bring the 1/3 to the front like ln|1-3y|^1/3 before removing the e??
    The 1/3 must remain in the log so that we can simplify : \exp\left(-\frac{1}{3}\ln |1-3y|\right) <br />
=\exp\left(\ln\left(|1-3y|^{-\frac{1}{3}} \right)\right)<br />
=|1-3y|^{-\frac{1}{3}}=\ldots. But, if you know that the definition of a^b is a^b=\exp(b\ln a), there is no need to do this and you can write down the result without any detail.


    btw how do you get the pi symbol above the toolbar for using lateX (dy/dx) etc?
    Maybe your looking for the symbol ? It's on the right of the toolbar, next to the Youtube icon.
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