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