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Simplifying 2ln(x + -2) = ln(x + 2) + ln(9) Reorder the terms: 2ln(-2 + x) = ln(x + 2) + ln(9) (-2 * 2ln + x * 2ln) = ln(x + 2) + ln(9) (-4ln + 2lnx) = ln(x + 2) + ln(9) Reorder the terms: -4ln + 2lnx = ln(2 + x) + ln(9) -4ln + 2lnx = (2 * ln + x * ln) + ln(9) -4ln + 2lnx = (2ln + lnx) + ln(9) Reorder the terms for easier multiplication: -4ln + 2lnx = 2ln + lnx + 9ln Reorder the terms: -4ln + 2lnx = 2ln + 9ln + lnx Combine like terms: 2ln + 9ln = 11ln -4ln + 2lnx = 11ln + lnx Solving -4ln + 2lnx = 11ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. -4ln + -11ln + 2lnx = 11ln + -11ln + lnx Combine like terms: -4ln + -11ln = -15ln -15ln + 2lnx = 11ln + -11ln + lnx Combine like terms: 11ln + -11ln = 0 -15ln + 2lnx = 0 + lnx -15ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -15ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -15ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -15ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + x) = 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 '(-15 + x)' equal to zero and attempt to solve: Simplifying -15 + x = 0 Solving -15 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + x = 0 + 15 x = 0 + 15 Combine like terms: 0 + 15 = 15 x = 15 Add '-1x' to each side of the equation. x + -1x = 15 + -1x Combine like terms: x + -1x = 0 0 = 15 + -1x Simplifying 0 = 15 + -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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