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Simplifying 2ln(x + 5) + -1ln(2x + -5) = ln(x + 9) Reorder the terms: 2ln(5 + x) + -1ln(2x + -5) = ln(x + 9) (5 * 2ln + x * 2ln) + -1ln(2x + -5) = ln(x + 9) (10ln + 2lnx) + -1ln(2x + -5) = ln(x + 9) Reorder the terms: 10ln + 2lnx + -1ln(-5 + 2x) = ln(x + 9) 10ln + 2lnx + (-5 * -1ln + 2x * -1ln) = ln(x + 9) 10ln + 2lnx + (5ln + -2lnx) = ln(x + 9) Reorder the terms: 10ln + 5ln + 2lnx + -2lnx = ln(x + 9) Combine like terms: 10ln + 5ln = 15ln 15ln + 2lnx + -2lnx = ln(x + 9) Combine like terms: 2lnx + -2lnx = 0 15ln + 0 = ln(x + 9) 15ln = ln(x + 9) Reorder the terms: 15ln = ln(9 + x) 15ln = (9 * ln + x * ln) 15ln = (9ln + lnx) Solving 15ln = 9ln + lnx 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. 15ln + -9ln = 9ln + -9ln + lnx Combine like terms: 15ln + -9ln = 6ln 6ln = 9ln + -9ln + lnx Combine like terms: 9ln + -9ln = 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), 'ln'. ln(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + x 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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