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Simplifying ln(x + 7) + -1ln(x + -5) = ln(x) Reorder the terms: ln(7 + x) + -1ln(x + -5) = ln(x) (7 * ln + x * ln) + -1ln(x + -5) = ln(x) (7ln + lnx) + -1ln(x + -5) = ln(x) Reorder the terms: 7ln + lnx + -1ln(-5 + x) = ln(x) 7ln + lnx + (-5 * -1ln + x * -1ln) = ln(x) 7ln + lnx + (5ln + -1lnx) = ln(x) Reorder the terms: 7ln + 5ln + lnx + -1lnx = ln(x) Combine like terms: 7ln + 5ln = 12ln 12ln + lnx + -1lnx = ln(x) Combine like terms: lnx + -1lnx = 0 12ln + 0 = ln(x) 12ln = ln(x) Multiply ln * x 12ln = lnx Solving 12ln = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 12ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 12ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(12 + -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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 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 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Add 'x' to each side of the equation. -1x + x = -12 + x Combine like terms: -1x + x = 0 0 = -12 + x Simplifying 0 = -12 + 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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