I am following an example in a book and it makes a jump that I cannot seem to follow. Please help me understand what steps were taken.

Starting Equation: $\displaystyle \frac{dp}{dt} = 0.5p - 450 \left(1\right)$

Which can be rewritten as:

$\displaystyle \frac{dp}{dt} = \frac{p-900}{2} \left(2\right)$

or if p != 900,

$\displaystyle \frac{\frac{dp}{dt}}{p-900} = \frac{1}{2} \left(3\right)$

Now heres where I get lost. They state that by the chain rule the left side of Eq. (3) is the derivative of $\displaystyle \ln |p-900|$ with respect to t, so we have:

$\displaystyle \frac{d}{dt} \ln |p-900| = \frac{1}{2} $

Any help is greatly appreciated.

Thanks.