f(x)=ln(2-x)-ln(4-x)

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Solution for f(x)=ln(2-x)-ln(4-x) equation: 


Simplifying
f(x) = ln(2 + -1x) + -1ln(4 + -1x)

Multiply f * x
fx = ln(2 + -1x) + -1ln(4 + -1x)
fx = (2 * ln + -1x * ln) + -1ln(4 + -1x)
fx = (2ln + -1lnx) + -1ln(4 + -1x)
fx = 2ln + -1lnx + (4 * -1ln + -1x * -1ln)
fx = 2ln + -1lnx + (-4ln + 1lnx)

Reorder the terms:
fx = 2ln + -4ln + -1lnx + 1lnx

Combine like terms: 2ln + -4ln = -2ln
fx = -2ln + -1lnx + 1lnx

Combine like terms: -1lnx + 1lnx = 0
fx = -2ln + 0
fx = -2ln

Solving
fx = -2ln

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -2lnx-1

Simplifying
f = -2lnx-1

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