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Simplifying 2ln(x + 3) = ln(12x) Reorder the terms: 2ln(3 + x) = ln(12x) (3 * 2ln + x * 2ln) = ln(12x) (6ln + 2lnx) = ln(12x) Remove parenthesis around (12x) 6ln + 2lnx = ln * 12x Reorder the terms for easier multiplication: 6ln + 2lnx = 12ln * x Multiply ln * x 6ln + 2lnx = 12lnx Solving 6ln + 2lnx = 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. 6ln + 2lnx + -12lnx = 12lnx + -12lnx Combine like terms: 2lnx + -12lnx = -10lnx 6ln + -10lnx = 12lnx + -12lnx Combine like terms: 12lnx + -12lnx = 0 6ln + -10lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(3 + -5x) = 0 Ignore the factor 2.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 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Add '5x' to each side of the equation. -5x + 5x = -3 + 5x Combine like terms: -5x + 5x = 0 0 = -3 + 5x Simplifying 0 = -3 + 5x 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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