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Simplifying ln(x + 2) + -1lnx = ln(x + 12) Reorder the terms: ln(2 + x) + -1lnx = ln(x + 12) (2 * ln + x * ln) + -1lnx = ln(x + 12) (2ln + lnx) + -1lnx = ln(x + 12) Combine like terms: lnx + -1lnx = 0 2ln + 0 = ln(x + 12) 2ln = ln(x + 12) Reorder the terms: 2ln = ln(12 + x) 2ln = (12 * ln + x * ln) 2ln = (12ln + lnx) Solving 2ln = 12ln + lnx 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. 2ln + -12ln = 12ln + -12ln + lnx Combine like terms: 2ln + -12ln = -10ln -10ln = 12ln + -12ln + lnx Combine like terms: 12ln + -12ln = 0 -10ln = 0 + lnx -10ln = lnx Add '-1lnx' to each side of the equation. -10ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -10ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -1x 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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