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Simplifying ln(x2 + 3) + -1ln(x + 1) = ln(5) Reorder the terms: ln(3 + x2) + -1ln(x + 1) = ln(5) (3 * ln + x2 * ln) + -1ln(x + 1) = ln(5) (3ln + lnx2) + -1ln(x + 1) = ln(5) Reorder the terms: 3ln + lnx2 + -1ln(1 + x) = ln(5) 3ln + lnx2 + (1 * -1ln + x * -1ln) = ln(5) 3ln + lnx2 + (-1ln + -1lnx) = ln(5) Reorder the terms: 3ln + -1ln + -1lnx + lnx2 = ln(5) Combine like terms: 3ln + -1ln = 2ln 2ln + -1lnx + lnx2 = ln(5) Reorder the terms for easier multiplication: 2ln + -1lnx + lnx2 = 5ln Solving 2ln + -1lnx + lnx2 = 5ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 2ln + -1lnx + -5ln + lnx2 = 5ln + -5ln Reorder the terms: 2ln + -5ln + -1lnx + lnx2 = 5ln + -5ln Combine like terms: 2ln + -5ln = -3ln -3ln + -1lnx + lnx2 = 5ln + -5ln Combine like terms: 5ln + -5ln = 0 -3ln + -1lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + -1x + x2) = 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 + -1x + x2)' equal to zero and attempt to solve: Simplifying -3 + -1x + x2 = 0 Solving -3 + -1x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -1x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x + x2 = 0 + 3 -1x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x + x2 = 3 Add 'x' to each side of the equation. -1x + x + x2 = 3 + x Combine like terms: -1x + x = 0 0 + x2 = 3 + x x2 = 3 + x Add '-1x2' to each side of the equation. x2 + -1x2 = 3 + x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 3 + x + -1x2 Simplifying 0 = 3 + x + -1x2 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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