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Simplifying ln(x + 2) + ln(x) = ln(12 + x) Reorder the terms: ln(2 + x) + ln(x) = ln(12 + x) (2 * ln + x * ln) + ln(x) = ln(12 + x) (2ln + lnx) + ln(x) = ln(12 + x) Multiply ln * x 2ln + lnx + lnx = ln(12 + x) Combine like terms: lnx + lnx = 2lnx 2ln + 2lnx = ln(12 + x) 2ln + 2lnx = (12 * ln + x * ln) 2ln + 2lnx = (12ln + lnx) Solving 2ln + 2lnx = 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 + 2lnx = 12ln + -12ln + lnx Combine like terms: 2ln + -12ln = -10ln -10ln + 2lnx = 12ln + -12ln + lnx Combine like terms: 12ln + -12ln = 0 -10ln + 2lnx = 0 + lnx -10ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -10ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -10ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -10ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + x) = 0Subproblem 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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