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Simplifying ln(x + -2) = ln(6) + -1ln(x + -3) Reorder the terms: ln(-2 + x) = ln(6) + -1ln(x + -3) (-2 * ln + x * ln) = ln(6) + -1ln(x + -3) (-2ln + lnx) = ln(6) + -1ln(x + -3) Reorder the terms for easier multiplication: -2ln + lnx = 6ln + -1ln(x + -3) Reorder the terms: -2ln + lnx = 6ln + -1ln(-3 + x) -2ln + lnx = 6ln + (-3 * -1ln + x * -1ln) -2ln + lnx = 6ln + (3ln + -1lnx) Combine like terms: 6ln + 3ln = 9ln -2ln + lnx = 9ln + -1lnx Solving -2ln + lnx = 9ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. -2ln + -9ln + lnx = 9ln + -9ln + -1lnx Combine like terms: -2ln + -9ln = -11ln -11ln + lnx = 9ln + -9ln + -1lnx Combine like terms: 9ln + -9ln = 0 -11ln + lnx = 0 + -1lnx -11ln + lnx = -1lnx Add 'lnx' to each side of the equation. -11ln + lnx + lnx = -1lnx + lnx Combine like terms: lnx + lnx = 2lnx -11ln + 2lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -11ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + 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 '(-11 + 2x)' equal to zero and attempt to solve: Simplifying -11 + 2x = 0 Solving -11 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 2x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2x = 0 + 11 2x = 0 + 11 Combine like terms: 0 + 11 = 11 2x = 11 Add '-2x' to each side of the equation. 2x + -2x = 11 + -2x Combine like terms: 2x + -2x = 0 0 = 11 + -2x Simplifying 0 = 11 + -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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