2ln(x)-ln(6-x)=ln(3)

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Solution for 2ln(x)-ln(6-x)=ln(3) equation:


Simplifying
2ln(x) + -1ln(6 + -1x) = ln(3)

Multiply ln * x
2lnx + -1ln(6 + -1x) = ln(3)
2lnx + (6 * -1ln + -1x * -1ln) = ln(3)
2lnx + (-6ln + 1lnx) = ln(3)

Reorder the terms:
-6ln + 2lnx + 1lnx = ln(3)

Combine like terms: 2lnx + 1lnx = 3lnx
-6ln + 3lnx = ln(3)

Reorder the terms for easier multiplication:
-6ln + 3lnx = 3ln

Solving
-6ln + 3lnx = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-6ln + -3ln + 3lnx = 3ln + -3ln

Combine like terms: -6ln + -3ln = -9ln
-9ln + 3lnx = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-9ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(-3 + x) = 0

Ignore the factor 3.

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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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