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Simplifying 2ln(x + 3) + -1ln(x + 1) = 3ln(2) Reorder the terms: 2ln(3 + x) + -1ln(x + 1) = 3ln(2) (3 * 2ln + x * 2ln) + -1ln(x + 1) = 3ln(2) (6ln + 2lnx) + -1ln(x + 1) = 3ln(2) Reorder the terms: 6ln + 2lnx + -1ln(1 + x) = 3ln(2) 6ln + 2lnx + (1 * -1ln + x * -1ln) = 3ln(2) 6ln + 2lnx + (-1ln + -1lnx) = 3ln(2) Reorder the terms: 6ln + -1ln + 2lnx + -1lnx = 3ln(2) Combine like terms: 6ln + -1ln = 5ln 5ln + 2lnx + -1lnx = 3ln(2) Combine like terms: 2lnx + -1lnx = 1lnx 5ln + 1lnx = 3ln(2) Reorder the terms for easier multiplication: 5ln + 1lnx = 3 * 2ln Multiply 3 * 2 5ln + 1lnx = 6ln Solving 5ln + 1lnx = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 5ln + -6ln + 1lnx = 6ln + -6ln Combine like terms: 5ln + -6ln = -1ln -1ln + 1lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -1ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1 + 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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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