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Simplifying ln(12 + -2x) + -2ln(x) = ln(2) (12 * ln + -2x * ln) + -2ln(x) = ln(2) (12ln + -2lnx) + -2ln(x) = ln(2) Multiply ln * x 12ln + -2lnx + -2lnx = ln(2) Combine like terms: -2lnx + -2lnx = -4lnx 12ln + -4lnx = ln(2) Reorder the terms for easier multiplication: 12ln + -4lnx = 2ln Solving 12ln + -4lnx = 2ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. 12ln + -2ln + -4lnx = 2ln + -2ln Combine like terms: 12ln + -2ln = 10ln 10ln + -4lnx = 2ln + -2ln Combine like terms: 2ln + -2ln = 0 10ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(5 + -2x) = 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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Add '2x' to each side of the equation. -2x + 2x = -5 + 2x Combine like terms: -2x + 2x = 0 0 = -5 + 2x Simplifying 0 = -5 + 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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