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Simplifying ln(x2 + -7) = ln(3 + -3x) Reorder the terms: ln(-7 + x2) = ln(3 + -3x) (-7 * ln + x2 * ln) = ln(3 + -3x) (-7ln + lnx2) = ln(3 + -3x) -7ln + lnx2 = (3 * ln + -3x * ln) -7ln + lnx2 = (3ln + -3lnx) Solving -7ln + lnx2 = 3ln + -3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. -7ln + -3ln + lnx2 = 3ln + -3ln + -3lnx Combine like terms: -7ln + -3ln = -10ln -10ln + lnx2 = 3ln + -3ln + -3lnx Combine like terms: 3ln + -3ln = 0 -10ln + lnx2 = 0 + -3lnx -10ln + lnx2 = -3lnx Add '3lnx' to each side of the equation. -10ln + 3lnx + lnx2 = -3lnx + 3lnx Combine like terms: -3lnx + 3lnx = 0 -10ln + 3lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + 3x + x2) = 0 Factor a trinomial. ln((-5 + -1x)(2 + -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 '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Add 'x' to each side of the equation. -1x + x = 5 + x Combine like terms: -1x + x = 0 0 = 5 + x Simplifying 0 = 5 + 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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