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Simplifying ln(x + -2) = ln(12x) Reorder the terms: ln(-2 + x) = ln(12x) (-2 * ln + x * ln) = ln(12x) (-2ln + lnx) = ln(12x) Remove parenthesis around (12x) -2ln + lnx = ln * 12x Reorder the terms for easier multiplication: -2ln + lnx = 12ln * x Multiply ln * x -2ln + lnx = 12lnx Solving -2ln + lnx = 12lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12lnx' to each side of the equation. -2ln + lnx + -12lnx = 12lnx + -12lnx Combine like terms: lnx + -12lnx = -11lnx -2ln + -11lnx = 12lnx + -12lnx Combine like terms: 12lnx + -12lnx = 0 -2ln + -11lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(2 + 11x) = 0 Ignore the factor -1.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 + 11x)' equal to zero and attempt to solve: Simplifying 2 + 11x = 0 Solving 2 + 11x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 11x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 11x = 0 + -2 11x = 0 + -2 Combine like terms: 0 + -2 = -2 11x = -2 Add '-11x' to each side of the equation. 11x + -11x = -2 + -11x Combine like terms: 11x + -11x = 0 0 = -2 + -11x Simplifying 0 = -2 + -11x 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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