To find the area bounded by these curves, we first need to determine the interval over which the curves intersect each other.

First, let's consider the curves y = ln x and y = ln|x|. These two curves intersect when ln x = ln|x|. Taking exponentials of both sides, we have x = |x|.

Solving this equation, we find that x = 1 or x = -1. Therefore, the curves intersect at x = 1 and x = -1.

Next, let's consider the curves y = ln x and y = |ln x|. These two curves intersect when ln x = |ln x|. We can split this equation into two cases:

Case 1: ln x = ln x
In this case, the equation is true for all x except x = 0.

Case 2: ln x = -ln x
In this case, taking exponentials of both sides, we have x = 1. However, since x = 1 is already included in Case 1, there is no additional intersection point.

Therefore, the curves y = ln x and y = |ln x| intersect at all x except x = 0.

Finally, let's consider the curves y = ln|x| and y = |ln|x||. These two curves intersect when ln|x| = |ln|x||. We can split this equation into two cases:

Case 1: ln|x| = ln|x|
In this case, the equation is true for all x except x = 0.

Case 2: ln|x| = -ln|x|
In this case, taking exponentials of both sides, we have |x| = 1. This equation is true for x = 1 and x = -1.

Therefore, the curves y = ln|x| and y = |ln|x|| intersect at x = 1, x = -1, and all x except x = 0.

Now that we have determined the interval over which the curves intersect, we can proceed to find the area bounded by these curves.

First, we can consider the region bounded by the curves y = ln x, y = ln|x|, and the x-axis. This region lies to the right of x = 1 and to the left of x = -1. We can find the area of this region by integrating the difference between the curves y = ln x and y = ln|x| over this interval:

∫(ln x - ln|x|) dx from x = -1 to x = 1

This integral evaluates to 2.

Next, we can consider the region bounded by the curves y = ln|x|, y = |ln x|, and the x-axis. This region lies to the right of x = 1 and to the left of x = 0. We can find the area of this region by integrating the difference between the curves y = ln|x| and y = |ln x| over this interval:

∫(ln|x| - |ln x|) dx from x = 0 to x = 1

This integral evaluates to 1/2.

Finally, we can consider the region bounded by the curves y = |ln x|, y = |ln|x||, and the x-axis. This region lies to the right of x = 1. We can find the area of this region by integrating the difference between the curves