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Simplifying ln(6 + -1x) + ln(-5 + -1x) = ln(3 + -9x) (6 * ln + -1x * ln) + ln(-5 + -1x) = ln(3 + -9x) (6ln + -1lnx) + ln(-5 + -1x) = ln(3 + -9x) 6ln + -1lnx + (-5 * ln + -1x * ln) = ln(3 + -9x) 6ln + -1lnx + (-5ln + -1lnx) = ln(3 + -9x) Reorder the terms: 6ln + -5ln + -1lnx + -1lnx = ln(3 + -9x) Combine like terms: 6ln + -5ln = 1ln 1ln + -1lnx + -1lnx = ln(3 + -9x) Combine like terms: -1lnx + -1lnx = -2lnx 1ln + -2lnx = ln(3 + -9x) 1ln + -2lnx = (3 * ln + -9x * ln) 1ln + -2lnx = (3ln + -9lnx) Solving 1ln + -2lnx = 3ln + -9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 1ln + -3ln + -2lnx = 3ln + -3ln + -9lnx Combine like terms: 1ln + -3ln = -2ln -2ln + -2lnx = 3ln + -3ln + -9lnx Combine like terms: 3ln + -3ln = 0 -2ln + -2lnx = 0 + -9lnx -2ln + -2lnx = -9lnx Add '9lnx' to each side of the equation. -2ln + -2lnx + 9lnx = -9lnx + 9lnx Combine like terms: -2lnx + 9lnx = 7lnx -2ln + 7lnx = -9lnx + 9lnx Combine like terms: -9lnx + 9lnx = 0 -2ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + 7x) = 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 '(-2 + 7x)' equal to zero and attempt to solve: Simplifying -2 + 7x = 0 Solving -2 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 7x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7x = 0 + 2 7x = 0 + 2 Combine like terms: 0 + 2 = 2 7x = 2 Add '-7x' to each side of the equation. 7x + -7x = 2 + -7x Combine like terms: 7x + -7x = 0 0 = 2 + -7x Simplifying 0 = 2 + -7x 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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