Question

I need to graph these equations:
y = abs(lnx) and y=ln abs(x)
i don't know the difference with the absolute values. please help :(

Answer 1

The difference lies in the placement of the absolute values and the order of operations.
The absolute value essentially gives the positive value of the expression contained inside them, and act as parentheses in terms of the order of operations.

Answer 2

If we consider that, then we can say some things about these functions (also retriceing we know y = ln(x)):

y = abs(ln x) means that any possible negative value of ln(x) will become positive. These negative values occur when 0 < x < 1, so all the numbers in this region will be reflected over the x-axis to make it positive.

y = ln(abs(x)) means that any negative value of x is made positive, while sustaining the same value for any positive x-value. Because both the positive value and its opposite return the same value, it is essentially the natural log function flipped over the y-axis.

If it is still not clear, you may want to test some (x,y) points to make out the graphs for yourself. If you follow the order correctly, it should work out.