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