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Simplifying ln(7 + -1x) + ln(-4 + -1x) = ln(2 + -4x) (7 * ln + -1x * ln) + ln(-4 + -1x) = ln(2 + -4x) (7ln + -1lnx) + ln(-4 + -1x) = ln(2 + -4x) 7ln + -1lnx + (-4 * ln + -1x * ln) = ln(2 + -4x) 7ln + -1lnx + (-4ln + -1lnx) = ln(2 + -4x) Reorder the terms: 7ln + -4ln + -1lnx + -1lnx = ln(2 + -4x) Combine like terms: 7ln + -4ln = 3ln 3ln + -1lnx + -1lnx = ln(2 + -4x) Combine like terms: -1lnx + -1lnx = -2lnx 3ln + -2lnx = ln(2 + -4x) 3ln + -2lnx = (2 * ln + -4x * ln) 3ln + -2lnx = (2ln + -4lnx) Solving 3ln + -2lnx = 2ln + -4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. 3ln + -2ln + -2lnx = 2ln + -2ln + -4lnx Combine like terms: 3ln + -2ln = 1ln 1ln + -2lnx = 2ln + -2ln + -4lnx Combine like terms: 2ln + -2ln = 0 1ln + -2lnx = 0 + -4lnx 1ln + -2lnx = -4lnx Add '4lnx' to each side of the equation. 1ln + -2lnx + 4lnx = -4lnx + 4lnx Combine like terms: -2lnx + 4lnx = 2lnx 1ln + 2lnx = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 1ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -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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