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Simplifying ln(x + 4) + ln(x) = ln(x + 12) Reorder the terms: ln(4 + x) + ln(x) = ln(x + 12) (4 * ln + x * ln) + ln(x) = ln(x + 12) (4ln + lnx) + ln(x) = ln(x + 12) Multiply ln * x 4ln + lnx + lnx = ln(x + 12) Combine like terms: lnx + lnx = 2lnx 4ln + 2lnx = ln(x + 12) Reorder the terms: 4ln + 2lnx = ln(12 + x) 4ln + 2lnx = (12 * ln + x * ln) 4ln + 2lnx = (12ln + lnx) Solving 4ln + 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. 4ln + -12ln + 2lnx = 12ln + -12ln + lnx Combine like terms: 4ln + -12ln = -8ln -8ln + 2lnx = 12ln + -12ln + lnx Combine like terms: 12ln + -12ln = 0 -8ln + 2lnx = 0 + lnx -8ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -8ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -8ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -8ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -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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