ln(3)+ln(x)=ln(12-x)

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Solution for ln(3)+ln(x)=ln(12-x) equation:


Simplifying
ln(3) + ln(x) = ln(12 + -1x)

Reorder the terms for easier multiplication:
3ln + ln(x) = ln(12 + -1x)

Multiply ln * x
3ln + lnx = ln(12 + -1x)
3ln + lnx = (12 * ln + -1x * ln)
3ln + lnx = (12ln + -1lnx)

Solving
3ln + lnx = 12ln + -1lnx

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
3ln + -12ln + lnx = 12ln + -12ln + -1lnx

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

Combine like terms: 12ln + -12ln = 0
-9ln + lnx = 0 + -1lnx
-9ln + lnx = -1lnx

Add 'lnx' to each side of the equation.
-9ln + lnx + lnx = -1lnx + lnx

Combine like terms: lnx + lnx = 2lnx
-9ln + 2lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-9ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + 2x) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Add '-2x' to each side of the equation. 2x + -2x = 9 + -2x Combine like terms: 2x + -2x = 0 0 = 9 + -2x Simplifying 0 = 9 + -2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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