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