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Simplifying 6ln(2x + -2) + -3ln3(2x + -2) = 0 Reorder the terms: 6ln(-2 + 2x) + -3ln3(2x + -2) = 0 (-2 * 6ln + 2x * 6ln) + -3ln3(2x + -2) = 0 (-12ln + 12lnx) + -3ln3(2x + -2) = 0 Reorder the terms: -12ln + 12lnx + -3ln3(-2 + 2x) = 0 -12ln + 12lnx + (-2 * -3ln3 + 2x * -3ln3) = 0 -12ln + 12lnx + (6ln3 + -6ln3x) = 0 Solving -12ln + 12lnx + 6ln3 + -6ln3x = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(-2 + 2x + n2 + -1n2x) = 0 Ignore the factor 6.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 '(-2 + 2x + n2 + -1n2x)' equal to zero and attempt to solve: Simplifying -2 + 2x + n2 + -1n2x = 0 Reorder the terms: -2 + n2 + -1n2x + 2x = 0 Solving -2 + n2 + -1n2x + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + n2 + -1n2x + 2 + 2x = 0 + 2 Reorder the terms: -2 + 2 + n2 + -1n2x + 2x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + n2 + -1n2x + 2x = 0 + 2 n2 + -1n2x + 2x = 0 + 2 Combine like terms: 0 + 2 = 2 n2 + -1n2x + 2x = 2 Add '-1n2' to each side of the equation. n2 + -1n2x + -1n2 + 2x = 2 + -1n2 Reorder the terms: n2 + -1n2 + -1n2x + 2x = 2 + -1n2 Combine like terms: n2 + -1n2 = 0 0 + -1n2x + 2x = 2 + -1n2 -1n2x + 2x = 2 + -1n2 Add 'n2x' to each side of the equation. -1n2x + n2x + 2x = 2 + -1n2 + n2x Combine like terms: -1n2x + n2x = 0 0 + 2x = 2 + -1n2 + n2x 2x = 2 + -1n2 + n2x Add '-2x' to each side of the equation. 2x + -2x = 2 + -1n2 + n2x + -2x Combine like terms: 2x + -2x = 0 0 = 2 + -1n2 + n2x + -2x Simplifying 0 = 2 + -1n2 + n2x + -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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