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Simplifying ln(4x + -2) + ln(x + 3) = ln(4x2 + 15) Reorder the terms: ln(-2 + 4x) + ln(x + 3) = ln(4x2 + 15) (-2 * ln + 4x * ln) + ln(x + 3) = ln(4x2 + 15) (-2ln + 4lnx) + ln(x + 3) = ln(4x2 + 15) Reorder the terms: -2ln + 4lnx + ln(3 + x) = ln(4x2 + 15) -2ln + 4lnx + (3 * ln + x * ln) = ln(4x2 + 15) -2ln + 4lnx + (3ln + lnx) = ln(4x2 + 15) Reorder the terms: -2ln + 3ln + 4lnx + lnx = ln(4x2 + 15) Combine like terms: -2ln + 3ln = 1ln 1ln + 4lnx + lnx = ln(4x2 + 15) Combine like terms: 4lnx + lnx = 5lnx 1ln + 5lnx = ln(4x2 + 15) Reorder the terms: 1ln + 5lnx = ln(15 + 4x2) 1ln + 5lnx = (15 * ln + 4x2 * ln) 1ln + 5lnx = (15ln + 4lnx2) Solving 1ln + 5lnx = 15ln + 4lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 1ln + -15ln + 5lnx = 15ln + -15ln + 4lnx2 Combine like terms: 1ln + -15ln = -14ln -14ln + 5lnx = 15ln + -15ln + 4lnx2 Combine like terms: 15ln + -15ln = 0 -14ln + 5lnx = 0 + 4lnx2 -14ln + 5lnx = 4lnx2 Add '-4lnx2' to each side of the equation. -14ln + 5lnx + -4lnx2 = 4lnx2 + -4lnx2 Combine like terms: 4lnx2 + -4lnx2 = 0 -14ln + 5lnx + -4lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-14 + 5x + -4x2) = 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 '(-14 + 5x + -4x2)' equal to zero and attempt to solve: Simplifying -14 + 5x + -4x2 = 0 Solving -14 + 5x + -4x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 5x + 14 + -4x2 = 0 + 14 Reorder the terms: -14 + 14 + 5x + -4x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 5x + -4x2 = 0 + 14 5x + -4x2 = 0 + 14 Combine like terms: 0 + 14 = 14 5x + -4x2 = 14 Add '-5x' to each side of the equation. 5x + -5x + -4x2 = 14 + -5x Combine like terms: 5x + -5x = 0 0 + -4x2 = 14 + -5x -4x2 = 14 + -5x Add '4x2' to each side of the equation. -4x2 + 4x2 = 14 + -5x + 4x2 Combine like terms: -4x2 + 4x2 = 0 0 = 14 + -5x + 4x2 Simplifying 0 = 14 + -5x + 4x2 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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