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