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Simplifying ln(4 + -2x) + ln(9 + -3x) = 2ln(x + 1) (4 * ln + -2x * ln) + ln(9 + -3x) = 2ln(x + 1) (4ln + -2lnx) + ln(9 + -3x) = 2ln(x + 1) 4ln + -2lnx + (9 * ln + -3x * ln) = 2ln(x + 1) 4ln + -2lnx + (9ln + -3lnx) = 2ln(x + 1) Reorder the terms: 4ln + 9ln + -2lnx + -3lnx = 2ln(x + 1) Combine like terms: 4ln + 9ln = 13ln 13ln + -2lnx + -3lnx = 2ln(x + 1) Combine like terms: -2lnx + -3lnx = -5lnx 13ln + -5lnx = 2ln(x + 1) Reorder the terms: 13ln + -5lnx = 2ln(1 + x) 13ln + -5lnx = (1 * 2ln + x * 2ln) 13ln + -5lnx = (2ln + 2lnx) Solving 13ln + -5lnx = 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. 13ln + -2ln + -5lnx = 2ln + -2ln + 2lnx Combine like terms: 13ln + -2ln = 11ln 11ln + -5lnx = 2ln + -2ln + 2lnx Combine like terms: 2ln + -2ln = 0 11ln + -5lnx = 0 + 2lnx 11ln + -5lnx = 2lnx Add '-2lnx' to each side of the equation. 11ln + -5lnx + -2lnx = 2lnx + -2lnx Combine like terms: -5lnx + -2lnx = -7lnx 11ln + -7lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 11ln + -7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(11 + -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 '(11 + -7x)' equal to zero and attempt to solve: Simplifying 11 + -7x = 0 Solving 11 + -7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -7x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -7x = 0 + -11 -7x = 0 + -11 Combine like terms: 0 + -11 = -11 -7x = -11 Add '7x' to each side of the equation. -7x + 7x = -11 + 7x Combine like terms: -7x + 7x = 0 0 = -11 + 7x Simplifying 0 = -11 + 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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