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Simplifying ln(x2 + -70) = ln(x + 2) Reorder the terms: ln(-70 + x2) = ln(x + 2) (-70 * ln + x2 * ln) = ln(x + 2) (-70ln + lnx2) = ln(x + 2) Reorder the terms: -70ln + lnx2 = ln(2 + x) -70ln + lnx2 = (2 * ln + x * ln) -70ln + lnx2 = (2ln + lnx) Solving -70ln + 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. -70ln + -2ln + lnx2 = 2ln + -2ln + lnx Combine like terms: -70ln + -2ln = -72ln -72ln + lnx2 = 2ln + -2ln + lnx Combine like terms: 2ln + -2ln = 0 -72ln + lnx2 = 0 + lnx -72ln + lnx2 = lnx Add '-1lnx' to each side of the equation. -72ln + -1lnx + lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -72ln + -1lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-72 + -1x + x2) = 0 Factor a trinomial. ln((-8 + -1x)(9 + -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 '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 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 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Add 'x' to each side of the equation. -1x + x = 8 + x Combine like terms: -1x + x = 0 0 = 8 + x Simplifying 0 = 8 + 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + 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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