As the topic says, I need to simplify:
$\ln |x-x^2| - \ln |x-1| $
I don't know how to approach the problem at all. I'm not asking for the answer, but something to maybe get me going.
As the topic says, I need to simplify:
$\ln |x-x^2| - \ln |x-1| $
I don't know how to approach the problem at all. I'm not asking for the answer, but something to maybe get me going.
Remember that logarithms have some rules associated with them that help you simplify problems. The most common are: $\ln(ab) = \ln a + \ln b$ and $\ln(a/b) = \ln a - \ln b$. The second one is the key to your problem. If you have the difference of logs, say $\ln a - \ln b$ then you can simplify it to be the log of a quotient: $\ln(a/b)$. If you have a quotient of polynomials, then you should be trying to factorise and eliminate common factors. For example:
$ \frac{x^2-x}{x-1} = \frac{x(x-1)}{x-1} = \ ? $
You want to simplify $\ln |x^2-x| - \ln |x-1|,$ so apply the two steps that I suggest.
Hint: can you factor $x-x^2$ then use the laws of logs?