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