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