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Simplifying ln(2x + -3) + ln(x + 4) = ln(2x2 + 11) Reorder the terms: ln(-3 + 2x) + ln(x + 4) = ln(2x2 + 11) (-3 * ln + 2x * ln) + ln(x + 4) = ln(2x2 + 11) (-3ln + 2lnx) + ln(x + 4) = ln(2x2 + 11) Reorder the terms: -3ln + 2lnx + ln(4 + x) = ln(2x2 + 11) -3ln + 2lnx + (4 * ln + x * ln) = ln(2x2 + 11) -3ln + 2lnx + (4ln + lnx) = ln(2x2 + 11) Reorder the terms: -3ln + 4ln + 2lnx + lnx = ln(2x2 + 11) Combine like terms: -3ln + 4ln = 1ln 1ln + 2lnx + lnx = ln(2x2 + 11) Combine like terms: 2lnx + lnx = 3lnx 1ln + 3lnx = ln(2x2 + 11) Reorder the terms: 1ln + 3lnx = ln(11 + 2x2) 1ln + 3lnx = (11 * ln + 2x2 * ln) 1ln + 3lnx = (11ln + 2lnx2) Solving 1ln + 3lnx = 11ln + 2lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. 1ln + -11ln + 3lnx = 11ln + -11ln + 2lnx2 Combine like terms: 1ln + -11ln = -10ln -10ln + 3lnx = 11ln + -11ln + 2lnx2 Combine like terms: 11ln + -11ln = 0 -10ln + 3lnx = 0 + 2lnx2 -10ln + 3lnx = 2lnx2 Add '-2lnx2' to each side of the equation. -10ln + 3lnx + -2lnx2 = 2lnx2 + -2lnx2 Combine like terms: 2lnx2 + -2lnx2 = 0 -10ln + 3lnx + -2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + 3x + -2x2) = 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 '(-10 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying -10 + 3x + -2x2 = 0 Solving -10 + 3x + -2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 3x + 10 + -2x2 = 0 + 10 Reorder the terms: -10 + 10 + 3x + -2x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 3x + -2x2 = 0 + 10 3x + -2x2 = 0 + 10 Combine like terms: 0 + 10 = 10 3x + -2x2 = 10 Add '-3x' to each side of the equation. 3x + -3x + -2x2 = 10 + -3x Combine like terms: 3x + -3x = 0 0 + -2x2 = 10 + -3x -2x2 = 10 + -3x Add '2x2' to each side of the equation. -2x2 + 2x2 = 10 + -3x + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 = 10 + -3x + 2x2 Simplifying 0 = 10 + -3x + 2x2 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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