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Simplifying ln(4x + -2) + ln(9 + -3x) = 2ln(x + 1) Reorder the terms: ln(-2 + 4x) + ln(9 + -3x) = 2ln(x + 1) (-2 * ln + 4x * ln) + ln(9 + -3x) = 2ln(x + 1) (-2ln + 4lnx) + ln(9 + -3x) = 2ln(x + 1) -2ln + 4lnx + (9 * ln + -3x * ln) = 2ln(x + 1) -2ln + 4lnx + (9ln + -3lnx) = 2ln(x + 1) Reorder the terms: -2ln + 9ln + 4lnx + -3lnx = 2ln(x + 1) Combine like terms: -2ln + 9ln = 7ln 7ln + 4lnx + -3lnx = 2ln(x + 1) Combine like terms: 4lnx + -3lnx = 1lnx 7ln + 1lnx = 2ln(x + 1) Reorder the terms: 7ln + 1lnx = 2ln(1 + x) 7ln + 1lnx = (1 * 2ln + x * 2ln) 7ln + 1lnx = (2ln + 2lnx) Solving 7ln + 1lnx = 2ln + 2lnx 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. 7ln + -2ln + 1lnx = 2ln + -2ln + 2lnx Combine like terms: 7ln + -2ln = 5ln 5ln + 1lnx = 2ln + -2ln + 2lnx Combine like terms: 2ln + -2ln = 0 5ln + 1lnx = 0 + 2lnx 5ln + 1lnx = 2lnx Add '-2lnx' to each side of the equation. 5ln + 1lnx + -2lnx = 2lnx + -2lnx Combine like terms: 1lnx + -2lnx = -1lnx 5ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 5ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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