f(x)=ln(1+exp(x))

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Solution for f(x)=ln(1+exp(x)) equation: 


Simplifying
f(x) = ln(1 + exp(x))

Multiply f * x
fx = ln(1 + exp(x))

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

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

Solving
fx = elnpx2 + 1ln

Solving for variable 'f'.

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

Divide each side by 'x'.
f = elnpx + lnx-1

Simplifying
f = elnpx + lnx-1

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