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Simplifying ln(2x2 + -7) = ln(x2 + 6x) Reorder the terms: ln(-7 + 2x2) = ln(x2 + 6x) (-7 * ln + 2x2 * ln) = ln(x2 + 6x) (-7ln + 2lnx2) = ln(x2 + 6x) Reorder the terms: -7ln + 2lnx2 = ln(6x + x2) -7ln + 2lnx2 = (6x * ln + x2 * ln) -7ln + 2lnx2 = (6lnx + lnx2) Solving -7ln + 2lnx2 = 6lnx + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx' to each side of the equation. -7ln + -6lnx + 2lnx2 = 6lnx + -6lnx + lnx2 Combine like terms: 6lnx + -6lnx = 0 -7ln + -6lnx + 2lnx2 = 0 + lnx2 -7ln + -6lnx + 2lnx2 = lnx2 Add '-1lnx2' to each side of the equation. -7ln + -6lnx + 2lnx2 + -1lnx2 = lnx2 + -1lnx2 Combine like terms: 2lnx2 + -1lnx2 = 1lnx2 -7ln + -6lnx + 1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -7ln + -6lnx + 1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + -6x + x2) = 0 Factor a trinomial. ln((-1 + -1x)(7 + -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 '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + 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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + 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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