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Simplifying ln(6x + 2) + -1ln(x + 1) = ln(2x + -1) Reorder the terms: ln(2 + 6x) + -1ln(x + 1) = ln(2x + -1) (2 * ln + 6x * ln) + -1ln(x + 1) = ln(2x + -1) (2ln + 6lnx) + -1ln(x + 1) = ln(2x + -1) Reorder the terms: 2ln + 6lnx + -1ln(1 + x) = ln(2x + -1) 2ln + 6lnx + (1 * -1ln + x * -1ln) = ln(2x + -1) 2ln + 6lnx + (-1ln + -1lnx) = ln(2x + -1) Reorder the terms: 2ln + -1ln + 6lnx + -1lnx = ln(2x + -1) Combine like terms: 2ln + -1ln = 1ln 1ln + 6lnx + -1lnx = ln(2x + -1) Combine like terms: 6lnx + -1lnx = 5lnx 1ln + 5lnx = ln(2x + -1) Reorder the terms: 1ln + 5lnx = ln(-1 + 2x) 1ln + 5lnx = (-1 * ln + 2x * ln) 1ln + 5lnx = (-1ln + 2lnx) Solving 1ln + 5lnx = -1ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 1ln + ln + 5lnx = -1ln + ln + 2lnx Combine like terms: 1ln + ln = 2ln 2ln + 5lnx = -1ln + ln + 2lnx Combine like terms: -1ln + ln = 0 2ln + 5lnx = 0 + 2lnx 2ln + 5lnx = 2lnx Add '-2lnx' to each side of the equation. 2ln + 5lnx + -2lnx = 2lnx + -2lnx Combine like terms: 5lnx + -2lnx = 3lnx 2ln + 3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 2ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2 + 3x) = 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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Add '-3x' to each side of the equation. 3x + -3x = -2 + -3x Combine like terms: 3x + -3x = 0 0 = -2 + -3x Simplifying 0 = -2 + -3x 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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