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Simplifying ln(4x + -2) + -1ln(8) = ln(x + -2) Reorder the terms: ln(-2 + 4x) + -1ln(8) = ln(x + -2) (-2 * ln + 4x * ln) + -1ln(8) = ln(x + -2) (-2ln + 4lnx) + -1ln(8) = ln(x + -2) Reorder the terms for easier multiplication: -2ln + 4lnx + -1 * 8ln = ln(x + -2) Multiply -1 * 8 -2ln + 4lnx + -8ln = ln(x + -2) Reorder the terms: -2ln + -8ln + 4lnx = ln(x + -2) Combine like terms: -2ln + -8ln = -10ln -10ln + 4lnx = ln(x + -2) Reorder the terms: -10ln + 4lnx = ln(-2 + x) -10ln + 4lnx = (-2 * ln + x * ln) -10ln + 4lnx = (-2ln + lnx) Solving -10ln + 4lnx = -2ln + lnx 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. -10ln + 2ln + 4lnx = -2ln + 2ln + lnx Combine like terms: -10ln + 2ln = -8ln -8ln + 4lnx = -2ln + 2ln + lnx Combine like terms: -2ln + 2ln = 0 -8ln + 4lnx = 0 + lnx -8ln + 4lnx = lnx Add '-1lnx' to each side of the equation. -8ln + 4lnx + -1lnx = lnx + -1lnx Combine like terms: 4lnx + -1lnx = 3lnx -8ln + 3lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -8ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 3x) = 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 + 3x)' equal to zero and attempt to solve: Simplifying -8 + 3x = 0 Solving -8 + 3x = 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 + 3x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3x = 0 + 8 3x = 0 + 8 Combine like terms: 0 + 8 = 8 3x = 8 Add '-3x' to each side of the equation. 3x + -3x = 8 + -3x Combine like terms: 3x + -3x = 0 0 = 8 + -3x Simplifying 0 = 8 + -3x 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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