Can you find the domain of ln|cos(x)|

If possible, please show steps too. Thanks.

the domain of ln u is u > 0

the range of | cos x | is 0 <= y <= 1
so we need to eliminate the points where cos x = 0

these are x = pi/2 + n * pi, where n is an integer

thus, the domain is x =/= pi/2 + n * pi
(all real numbers such that cos x =/= 0, so that | cos x | > 0)

The argument of a logarithm must be positive.
|cos(x)| ≥ 0
cos(x) ≠ 0
x ≠ integer multiples of π/2 or 3π/2

ln cant be 0 or negative, but since theres an absolute value, we only need to worry about when cosx = 0.
cosx = 0 at pi/2 + npi
so therefore your domain would be:
(pi)/2 + n(pi)