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Simplifying ln(x + -4) + ln(x + 2) = ln(x + 10) Reorder the terms: ln(-4 + x) + ln(x + 2) = ln(x + 10) (-4 * ln + x * ln) + ln(x + 2) = ln(x + 10) (-4ln + lnx) + ln(x + 2) = ln(x + 10) Reorder the terms: -4ln + lnx + ln(2 + x) = ln(x + 10) -4ln + lnx + (2 * ln + x * ln) = ln(x + 10) -4ln + lnx + (2ln + lnx) = ln(x + 10) Reorder the terms: -4ln + 2ln + lnx + lnx = ln(x + 10) Combine like terms: -4ln + 2ln = -2ln -2ln + lnx + lnx = ln(x + 10) Combine like terms: lnx + lnx = 2lnx -2ln + 2lnx = ln(x + 10) Reorder the terms: -2ln + 2lnx = ln(10 + x) -2ln + 2lnx = (10 * ln + x * ln) -2ln + 2lnx = (10ln + lnx) Solving -2ln + 2lnx = 10ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -2ln + -10ln + 2lnx = 10ln + -10ln + lnx Combine like terms: -2ln + -10ln = -12ln -12ln + 2lnx = 10ln + -10ln + lnx Combine like terms: 10ln + -10ln = 0 -12ln + 2lnx = 0 + lnx -12ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -12ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -12ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -12ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-12 + 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 '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Add '-1x' to each side of the equation. x + -1x = 12 + -1x Combine like terms: x + -1x = 0 0 = 12 + -1x Simplifying 0 = 12 + -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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