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Simplifying ln(3x + 1) + -1ln(x + -5) = 0 Reorder the terms: ln(1 + 3x) + -1ln(x + -5) = 0 (1 * ln + 3x * ln) + -1ln(x + -5) = 0 (1ln + 3lnx) + -1ln(x + -5) = 0 Reorder the terms: 1ln + 3lnx + -1ln(-5 + x) = 0 1ln + 3lnx + (-5 * -1ln + x * -1ln) = 0 1ln + 3lnx + (5ln + -1lnx) = 0 Reorder the terms: 1ln + 5ln + 3lnx + -1lnx = 0 Combine like terms: 1ln + 5ln = 6ln 6ln + 3lnx + -1lnx = 0 Combine like terms: 3lnx + -1lnx = 2lnx 6ln + 2lnx = 0 Solving 6ln + 2lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. 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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