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Simplifying ln(x + -8) = ln(x + -20) + -1lnx Reorder the terms: ln(-8 + x) = ln(x + -20) + -1lnx (-8 * ln + x * ln) = ln(x + -20) + -1lnx (-8ln + lnx) = ln(x + -20) + -1lnx Reorder the terms: -8ln + lnx = ln(-20 + x) + -1lnx -8ln + lnx = (-20 * ln + x * ln) + -1lnx -8ln + lnx = (-20ln + lnx) + -1lnx Combine like terms: lnx + -1lnx = 0 -8ln + lnx = -20ln + 0 -8ln + lnx = -20ln Solving -8ln + lnx = -20ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '20ln' to each side of the equation. -8ln + 20ln + lnx = -20ln + 20ln Combine like terms: -8ln + 20ln = 12ln 12ln + lnx = -20ln + 20ln Combine like terms: -20ln + 20ln = 0 12ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(12 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 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 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Add '-1x' to each side of the equation. x + -1x = -12 + -1x Combine like terms: x + -1x = 0 0 = -12 + -1x Simplifying 0 = -12 + -1x 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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