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Simplifying ln(4x + -2) + -1ln(4) = -1ln(x + -2) Reorder the terms: ln(-2 + 4x) + -1ln(4) = -1ln(x + -2) (-2 * ln + 4x * ln) + -1ln(4) = -1ln(x + -2) (-2ln + 4lnx) + -1ln(4) = -1ln(x + -2) Reorder the terms for easier multiplication: -2ln + 4lnx + -1 * 4ln = -1ln(x + -2) Multiply -1 * 4 -2ln + 4lnx + -4ln = -1ln(x + -2) Reorder the terms: -2ln + -4ln + 4lnx = -1ln(x + -2) Combine like terms: -2ln + -4ln = -6ln -6ln + 4lnx = -1ln(x + -2) Reorder the terms: -6ln + 4lnx = -1ln(-2 + x) -6ln + 4lnx = (-2 * -1ln + x * -1ln) -6ln + 4lnx = (2ln + -1lnx) Solving -6ln + 4lnx = 2ln + -1lnx 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. -6ln + -2ln + 4lnx = 2ln + -2ln + -1lnx Combine like terms: -6ln + -2ln = -8ln -8ln + 4lnx = 2ln + -2ln + -1lnx Combine like terms: 2ln + -2ln = 0 -8ln + 4lnx = 0 + -1lnx -8ln + 4lnx = -1lnx Add 'lnx' to each side of the equation. -8ln + 4lnx + lnx = -1lnx + lnx Combine like terms: 4lnx + lnx = 5lnx -8ln + 5lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -8ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 5x) = 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 '(-8 + 5x)' equal to zero and attempt to solve: Simplifying -8 + 5x = 0 Solving -8 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 5x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5x = 0 + 8 5x = 0 + 8 Combine like terms: 0 + 8 = 8 5x = 8 Add '-5x' to each side of the equation. 5x + -5x = 8 + -5x Combine like terms: 5x + -5x = 0 0 = 8 + -5x Simplifying 0 = 8 + -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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