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