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Simplifying ln(2x + 1) + ln(x + 3) = ln(x2 + -3x) Reorder the terms: ln(1 + 2x) + ln(x + 3) = ln(x2 + -3x) (1 * ln + 2x * ln) + ln(x + 3) = ln(x2 + -3x) (1ln + 2lnx) + ln(x + 3) = ln(x2 + -3x) Reorder the terms: 1ln + 2lnx + ln(3 + x) = ln(x2 + -3x) 1ln + 2lnx + (3 * ln + x * ln) = ln(x2 + -3x) 1ln + 2lnx + (3ln + lnx) = ln(x2 + -3x) Reorder the terms: 1ln + 3ln + 2lnx + lnx = ln(x2 + -3x) Combine like terms: 1ln + 3ln = 4ln 4ln + 2lnx + lnx = ln(x2 + -3x) Combine like terms: 2lnx + lnx = 3lnx 4ln + 3lnx = ln(x2 + -3x) Reorder the terms: 4ln + 3lnx = ln(-3x + x2) 4ln + 3lnx = (-3x * ln + x2 * ln) 4ln + 3lnx = (-3lnx + lnx2) Solving 4ln + 3lnx = -3lnx + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3lnx' to each side of the equation. 4ln + 3lnx + 3lnx = -3lnx + 3lnx + lnx2 Combine like terms: 3lnx + 3lnx = 6lnx 4ln + 6lnx = -3lnx + 3lnx + lnx2 Combine like terms: -3lnx + 3lnx = 0 4ln + 6lnx = 0 + lnx2 4ln + 6lnx = lnx2 Add '-1lnx2' to each side of the equation. 4ln + 6lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 4ln + 6lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(4 + 6x + -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 '(4 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + 6x + -1x2 = 0 Solving 4 + 6x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 6x + -4 + -1x2 = 0 + -4 Reorder the terms: 4 + -4 + 6x + -1x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6x + -1x2 = 0 + -4 6x + -1x2 = 0 + -4 Combine like terms: 0 + -4 = -4 6x + -1x2 = -4 Add '-6x' to each side of the equation. 6x + -6x + -1x2 = -4 + -6x Combine like terms: 6x + -6x = 0 0 + -1x2 = -4 + -6x -1x2 = -4 + -6x Add 'x2' to each side of the equation. -1x2 + x2 = -4 + -6x + x2 Combine like terms: -1x2 + x2 = 0 0 = -4 + -6x + x2 Simplifying 0 = -4 + -6x + 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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