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Simplifying ln(2x + -1) + -1ln(3x + 4) = ln(5x) Reorder the terms: ln(-1 + 2x) + -1ln(3x + 4) = ln(5x) (-1 * ln + 2x * ln) + -1ln(3x + 4) = ln(5x) (-1ln + 2lnx) + -1ln(3x + 4) = ln(5x) Reorder the terms: -1ln + 2lnx + -1ln(4 + 3x) = ln(5x) -1ln + 2lnx + (4 * -1ln + 3x * -1ln) = ln(5x) -1ln + 2lnx + (-4ln + -3lnx) = ln(5x) Reorder the terms: -1ln + -4ln + 2lnx + -3lnx = ln(5x) Combine like terms: -1ln + -4ln = -5ln -5ln + 2lnx + -3lnx = ln(5x) Combine like terms: 2lnx + -3lnx = -1lnx -5ln + -1lnx = ln(5x) Remove parenthesis around (5x) -5ln + -1lnx = ln * 5x Reorder the terms for easier multiplication: -5ln + -1lnx = 5ln * x Multiply ln * x -5ln + -1lnx = 5lnx Solving -5ln + -1lnx = 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5lnx' to each side of the equation. -5ln + -1lnx + -5lnx = 5lnx + -5lnx Combine like terms: -1lnx + -5lnx = -6lnx -5ln + -6lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -5ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(5 + 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 '(5 + 6x)' equal to zero and attempt to solve: Simplifying 5 + 6x = 0 Solving 5 + 6x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6x = 0 + -5 6x = 0 + -5 Combine like terms: 0 + -5 = -5 6x = -5 Add '-6x' to each side of the equation. 6x + -6x = -5 + -6x Combine like terms: 6x + -6x = 0 0 = -5 + -6x Simplifying 0 = -5 + -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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