=ln(1-exp(-x))

Solution for =ln(1-exp(-x)) equation:

Simplifying
0 = ln(1 + -1exp(-1x))

Remove parenthesis around (-1x)
0 = ln(1 + -1epx * -1x)

Reorder the terms for easier multiplication:
0 = ln(1 + -1 * -1epx * x)

Multiply -1 * -1
0 = ln(1 + 1epx * x)

Multiply epx * x
0 = ln(1 + 1epx2)
0 = (1 * ln + 1epx2 * ln)

Reorder the terms:
0 = (1elnpx2 + 1ln)
0 = (1elnpx2 + 1ln)

Solving
0 = 1elnpx2 + 1ln

Solving for variable 'e'.

Move all terms containing e to the left, all other terms to the right.

Add '-1elnpx2' to each side of the equation.
0 + -1elnpx2 = 1elnpx2 + -1elnpx2 + 1ln
Remove the zero:
-1elnpx2 = 1elnpx2 + -1elnpx2 + 1ln

Combine like terms: 1elnpx2 + -1elnpx2 = 0
-1elnpx2 = 0 + 1ln
-1elnpx2 = 1ln

Divide each side by '-1lnpx2'.
e = -1p-1x-2

Simplifying
e = -1p-1x-2