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Simplifying 2ln(x + 7) + -1ln(x + 3) = 4ln(2) Reorder the terms: 2ln(7 + x) + -1ln(x + 3) = 4ln(2) (7 * 2ln + x * 2ln) + -1ln(x + 3) = 4ln(2) (14ln + 2lnx) + -1ln(x + 3) = 4ln(2) Reorder the terms: 14ln + 2lnx + -1ln(3 + x) = 4ln(2) 14ln + 2lnx + (3 * -1ln + x * -1ln) = 4ln(2) 14ln + 2lnx + (-3ln + -1lnx) = 4ln(2) Reorder the terms: 14ln + -3ln + 2lnx + -1lnx = 4ln(2) Combine like terms: 14ln + -3ln = 11ln 11ln + 2lnx + -1lnx = 4ln(2) Combine like terms: 2lnx + -1lnx = 1lnx 11ln + 1lnx = 4ln(2) Reorder the terms for easier multiplication: 11ln + 1lnx = 4 * 2ln Multiply 4 * 2 11ln + 1lnx = 8ln Solving 11ln + 1lnx = 8ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 11ln + -8ln + 1lnx = 8ln + -8ln Combine like terms: 11ln + -8ln = 3ln 3ln + 1lnx = 8ln + -8ln Combine like terms: 8ln + -8ln = 0 3ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + x) = 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x 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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