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Simplifying 0.5ln(x2) + -1ln(x + 1) + ln(5) = ln(2x) Multiply ln * x2 0.5lnx2 + -1ln(x + 1) + ln(5) = ln(2x) Reorder the terms: 0.5lnx2 + -1ln(1 + x) + ln(5) = ln(2x) 0.5lnx2 + (1 * -1ln + x * -1ln) + ln(5) = ln(2x) 0.5lnx2 + (-1ln + -1lnx) + ln(5) = ln(2x) Reorder the terms for easier multiplication: 0.5lnx2 + -1ln + -1lnx + 5ln = ln(2x) Reorder the terms: -1ln + 5ln + -1lnx + 0.5lnx2 = ln(2x) Combine like terms: -1ln + 5ln = 4ln 4ln + -1lnx + 0.5lnx2 = ln(2x) Remove parenthesis around (2x) 4ln + -1lnx + 0.5lnx2 = ln * 2x Reorder the terms for easier multiplication: 4ln + -1lnx + 0.5lnx2 = 2ln * x Multiply ln * x 4ln + -1lnx + 0.5lnx2 = 2lnx Solving 4ln + -1lnx + 0.5lnx2 = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. 4ln + -1lnx + -2lnx + 0.5lnx2 = 2lnx + -2lnx Combine like terms: -1lnx + -2lnx = -3lnx 4ln + -3lnx + 0.5lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 4ln + -3lnx + 0.5lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(4 + -3x + 0.5x2) = 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 '(4 + -3x + 0.5x2)' equal to zero and attempt to solve: Simplifying 4 + -3x + 0.5x2 = 0 Solving 4 + -3x + 0.5x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -3x + -4 + 0.5x2 = 0 + -4 Reorder the terms: 4 + -4 + -3x + 0.5x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x + 0.5x2 = 0 + -4 -3x + 0.5x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3x + 0.5x2 = -4 Add '3x' to each side of the equation. -3x + 3x + 0.5x2 = -4 + 3x Combine like terms: -3x + 3x = 0 0 + 0.5x2 = -4 + 3x 0.5x2 = -4 + 3x Add '-0.5x2' to each side of the equation. 0.5x2 + -0.5x2 = -4 + 3x + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 0.0 = -4 + 3x + -0.5x2 Simplifying 0.0 = -4 + 3x + -0.5x2 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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