# Math Help - removing e,unsure of natural logs

1. ## removing e,unsure of natural logs

(-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?

2. Hi
Originally Posted by i_zz_y_ill

(-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 : $\exp\left(-\frac{1}{3}\ln |1-3y|\right)
=\exp\left(\ln\left(|1-3y|^{-\frac{1}{3}} \right)\right)
=|1-3y|^{-\frac{1}{3}}=\ldots$
. 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.