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Simplifying ln(-3x + -1) + -1ln(3x) = 0 Reorder the terms: ln(-1 + -3x) + -1ln(3x) = 0 (-1 * ln + -3x * ln) + -1ln(3x) = 0 (-1ln + -3lnx) + -1ln(3x) = 0 Remove parenthesis around (3x) -1ln + -3lnx + -1ln * 3x = 0 Reorder the terms for easier multiplication: -1ln + -3lnx + -1 * 3ln * x = 0 Multiply -1 * 3 -1ln + -3lnx + -3ln * x = 0 Multiply ln * x -1ln + -3lnx + -3lnx = 0 Combine like terms: -3lnx + -3lnx = -6lnx -1ln + -6lnx = 0 Solving -1ln + -6lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + 6x) = 0 Ignore the factor -1.Subproblem 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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