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Simplifying ln(8 + -1x3) + -1ln(2 + -1x) = ln(2x + 5) (8 * ln + -1x3 * ln) + -1ln(2 + -1x) = ln(2x + 5) (8ln + -1lnx3) + -1ln(2 + -1x) = ln(2x + 5) 8ln + -1lnx3 + (2 * -1ln + -1x * -1ln) = ln(2x + 5) 8ln + -1lnx3 + (-2ln + 1lnx) = ln(2x + 5) Reorder the terms: 8ln + -2ln + 1lnx + -1lnx3 = ln(2x + 5) Combine like terms: 8ln + -2ln = 6ln 6ln + 1lnx + -1lnx3 = ln(2x + 5) Reorder the terms: 6ln + 1lnx + -1lnx3 = ln(5 + 2x) 6ln + 1lnx + -1lnx3 = (5 * ln + 2x * ln) 6ln + 1lnx + -1lnx3 = (5ln + 2lnx) Solving 6ln + 1lnx + -1lnx3 = 5ln + 2lnx 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. 6ln + 1lnx + -5ln + -1lnx3 = 5ln + -5ln + 2lnx Reorder the terms: 6ln + -5ln + 1lnx + -1lnx3 = 5ln + -5ln + 2lnx Combine like terms: 6ln + -5ln = 1ln 1ln + 1lnx + -1lnx3 = 5ln + -5ln + 2lnx Combine like terms: 5ln + -5ln = 0 1ln + 1lnx + -1lnx3 = 0 + 2lnx 1ln + 1lnx + -1lnx3 = 2lnx Add '-2lnx' to each side of the equation. 1ln + 1lnx + -2lnx + -1lnx3 = 2lnx + -2lnx Combine like terms: 1lnx + -2lnx = -1lnx 1ln + -1lnx + -1lnx3 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 1ln + -1lnx + -1lnx3 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -1x + -1x3) = 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 + -1x + -1x3)' equal to zero and attempt to solve: Simplifying 1 + -1x + -1x3 = 0 Solving 1 + -1x + -1x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1x + -1 + -1x3 = 0 + -1 Reorder the terms: 1 + -1 + -1x + -1x3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x + -1x3 = 0 + -1 -1x + -1x3 = 0 + -1 Combine like terms: 0 + -1 = -1 -1x + -1x3 = -1 Add 'x' to each side of the equation. -1x + x + -1x3 = -1 + x Combine like terms: -1x + x = 0 0 + -1x3 = -1 + x -1x3 = -1 + x Add 'x3' to each side of the equation. -1x3 + x3 = -1 + x + x3 Combine like terms: -1x3 + x3 = 0 0 = -1 + x + x3 Simplifying 0 = -1 + x + x3 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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