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