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