f(x)=ln(x+9)-ln(x-3)

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Solution for f(x)=ln(x+9)-ln(x-3) equation: 


Simplifying
f(x) = ln(x + 9) + -1ln(x + -3)

Multiply f * x
fx = ln(x + 9) + -1ln(x + -3)

Reorder the terms:
fx = ln(9 + x) + -1ln(x + -3)
fx = (9 * ln + x * ln) + -1ln(x + -3)
fx = (9ln + lnx) + -1ln(x + -3)

Reorder the terms:
fx = 9ln + lnx + -1ln(-3 + x)
fx = 9ln + lnx + (-3 * -1ln + x * -1ln)
fx = 9ln + lnx + (3ln + -1lnx)

Reorder the terms:
fx = 9ln + 3ln + lnx + -1lnx

Combine like terms: 9ln + 3ln = 12ln
fx = 12ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
fx = 12ln + 0
fx = 12ln

Solving
fx = 12ln

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 12lnx-1

Simplifying
f = 12lnx-1

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