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Simplifying ln(x2 + -10) = ln(x + 2) Reorder the terms: ln(-10 + x2) = ln(x + 2) (-10 * ln + x2 * ln) = ln(x + 2) (-10ln + lnx2) = ln(x + 2) Reorder the terms: -10ln + lnx2 = ln(2 + x) -10ln + lnx2 = (2 * ln + x * ln) -10ln + lnx2 = (2ln + lnx) Solving -10ln + lnx2 = 2ln + lnx 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. -10ln + -2ln + lnx2 = 2ln + -2ln + lnx Combine like terms: -10ln + -2ln = -12ln -12ln + lnx2 = 2ln + -2ln + lnx Combine like terms: 2ln + -2ln = 0 -12ln + lnx2 = 0 + lnx -12ln + lnx2 = lnx Add '-1lnx' to each side of the equation. -12ln + -1lnx + lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -12ln + -1lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-12 + -1x + x2) = 0 Factor a trinomial. ln((-3 + -1x)(4 + -1x)) = 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 '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Add 'x' to each side of the equation. -1x + x = 3 + x Combine like terms: -1x + x = 0 0 = 3 + x Simplifying 0 = 3 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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