how do i sketch the graph of y=ln(|x|) ?

To sketch any modulus function, we begin with the sketch of the function itself, y=ln(x). Notice that the question asks for the graph of y=ln(|x|) and not y=|ln(x)|, this is an important distinction.recall that the absolute value always returns a positive value, regardless of the entry, so |x| is always positive, regardless of the sign of the x input. i.e. for x=-1, y=ln|-1|=ln(1), which is the same result as for x=1.so, the graph of y=ln(|x|) is the graph of y=ln(x) for x>0 and the reflection of this graph in line x=0, for x<0.