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Simplifying ln(3 + -1x) + ln(-2 + -1x) = ln(2 + -8x) (3 * ln + -1x * ln) + ln(-2 + -1x) = ln(2 + -8x) (3ln + -1lnx) + ln(-2 + -1x) = ln(2 + -8x) 3ln + -1lnx + (-2 * ln + -1x * ln) = ln(2 + -8x) 3ln + -1lnx + (-2ln + -1lnx) = ln(2 + -8x) Reorder the terms: 3ln + -2ln + -1lnx + -1lnx = ln(2 + -8x) Combine like terms: 3ln + -2ln = 1ln 1ln + -1lnx + -1lnx = ln(2 + -8x) Combine like terms: -1lnx + -1lnx = -2lnx 1ln + -2lnx = ln(2 + -8x) 1ln + -2lnx = (2 * ln + -8x * ln) 1ln + -2lnx = (2ln + -8lnx) Solving 1ln + -2lnx = 2ln + -8lnx 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. 1ln + -2ln + -2lnx = 2ln + -2ln + -8lnx Combine like terms: 1ln + -2ln = -1ln -1ln + -2lnx = 2ln + -2ln + -8lnx Combine like terms: 2ln + -2ln = 0 -1ln + -2lnx = 0 + -8lnx -1ln + -2lnx = -8lnx Add '8lnx' to each side of the equation. -1ln + -2lnx + 8lnx = -8lnx + 8lnx Combine like terms: -2lnx + 8lnx = 6lnx -1ln + 6lnx = -8lnx + 8lnx Combine like terms: -8lnx + 8lnx = 0 -1ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1 + 6x) = 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 + 6x)' equal to zero and attempt to solve: Simplifying -1 + 6x = 0 Solving -1 + 6x = 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 + 6x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6x = 0 + 1 6x = 0 + 1 Combine like terms: 0 + 1 = 1 6x = 1 Add '-6x' to each side of the equation. 6x + -6x = 1 + -6x Combine like terms: 6x + -6x = 0 0 = 1 + -6x Simplifying 0 = 1 + -6x 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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