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Simplifying ln(12x + -6) = ln * 12 Reorder the terms: ln(-6 + 12x) = ln * 12 (-6 * ln + 12x * ln) = ln * 12 (-6ln + 12lnx) = ln * 12 Reorder the terms for easier multiplication: -6ln + 12lnx = 12ln Solving -6ln + 12lnx = 12ln 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. -6ln + -12ln + 12lnx = 12ln + -12ln Combine like terms: -6ln + -12ln = -18ln -18ln + 12lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -18ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(-3 + 2x) = 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 '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -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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