And y=ln|x| is an even function, which is symmetrical about the ordinate (because ln|-x|=ln|x|, y = ln | x | is an even function).

So y = ln | x | is an even function with a range of r.

The natural logarithm is the logarithm with the constant e as the base, and it is denoted as lnn(n >；; 0)。 It is of great significance in physics, biology and other natural sciences, and is generally expressed as lnx.

The image of y=lnx is as shown in the figure:

The function about the origin symmetry is odd function, and the function about the Y axis symmetry is even.

If f(x) is an even function, then f(x+a)=f[-(x+a)]

But if f(x+a) is an even function, then f(x+a)=f(-x+a).

The image of y = ln | x | is as follows: