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Simplifying ln(8 + -1x) = ln(3x + -2) + ln(x + -2) (8 * ln + -1x * ln) = ln(3x + -2) + ln(x + -2) (8ln + -1lnx) = ln(3x + -2) + ln(x + -2) Reorder the terms: 8ln + -1lnx = ln(-2 + 3x) + ln(x + -2) 8ln + -1lnx = (-2 * ln + 3x * ln) + ln(x + -2) 8ln + -1lnx = (-2ln + 3lnx) + ln(x + -2) Reorder the terms: 8ln + -1lnx = -2ln + 3lnx + ln(-2 + x) 8ln + -1lnx = -2ln + 3lnx + (-2 * ln + x * ln) 8ln + -1lnx = -2ln + 3lnx + (-2ln + lnx) Reorder the terms: 8ln + -1lnx = -2ln + -2ln + 3lnx + lnx Combine like terms: -2ln + -2ln = -4ln 8ln + -1lnx = -4ln + 3lnx + lnx Combine like terms: 3lnx + lnx = 4lnx 8ln + -1lnx = -4ln + 4lnx Solving 8ln + -1lnx = -4ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4ln' to each side of the equation. 8ln + 4ln + -1lnx = -4ln + 4ln + 4lnx Combine like terms: 8ln + 4ln = 12ln 12ln + -1lnx = -4ln + 4ln + 4lnx Combine like terms: -4ln + 4ln = 0 12ln + -1lnx = 0 + 4lnx 12ln + -1lnx = 4lnx Add '-4lnx' to each side of the equation. 12ln + -1lnx + -4lnx = 4lnx + -4lnx Combine like terms: -1lnx + -4lnx = -5lnx 12ln + -5lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 12ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(12 + -5x) = 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 + -5x)' equal to zero and attempt to solve: Simplifying 12 + -5x = 0 Solving 12 + -5x = 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 + -5x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5x = 0 + -12 -5x = 0 + -12 Combine like terms: 0 + -12 = -12 -5x = -12 Add '5x' to each side of the equation. -5x + 5x = -12 + 5x Combine like terms: -5x + 5x = 0 0 = -12 + 5x Simplifying 0 = -12 + 5x 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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