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Simplifying ln(x + 2) + ln(x + -3) = ln(4x + -14) Reorder the terms: ln(2 + x) + ln(x + -3) = ln(4x + -14) (2 * ln + x * ln) + ln(x + -3) = ln(4x + -14) (2ln + lnx) + ln(x + -3) = ln(4x + -14) Reorder the terms: 2ln + lnx + ln(-3 + x) = ln(4x + -14) 2ln + lnx + (-3 * ln + x * ln) = ln(4x + -14) 2ln + lnx + (-3ln + lnx) = ln(4x + -14) Reorder the terms: 2ln + -3ln + lnx + lnx = ln(4x + -14) Combine like terms: 2ln + -3ln = -1ln -1ln + lnx + lnx = ln(4x + -14) Combine like terms: lnx + lnx = 2lnx -1ln + 2lnx = ln(4x + -14) Reorder the terms: -1ln + 2lnx = ln(-14 + 4x) -1ln + 2lnx = (-14 * ln + 4x * ln) -1ln + 2lnx = (-14ln + 4lnx) Solving -1ln + 2lnx = -14ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '14ln' to each side of the equation. -1ln + 14ln + 2lnx = -14ln + 14ln + 4lnx Combine like terms: -1ln + 14ln = 13ln 13ln + 2lnx = -14ln + 14ln + 4lnx Combine like terms: -14ln + 14ln = 0 13ln + 2lnx = 0 + 4lnx 13ln + 2lnx = 4lnx Add '-4lnx' to each side of the equation. 13ln + 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx 13ln + -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 13ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(13 + -2x) = 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 '(13 + -2x)' equal to zero and attempt to solve: Simplifying 13 + -2x = 0 Solving 13 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2x = 0 + -13 -2x = 0 + -13 Combine like terms: 0 + -13 = -13 -2x = -13 Add '2x' to each side of the equation. -2x + 2x = -13 + 2x Combine like terms: -2x + 2x = 0 0 = -13 + 2x Simplifying 0 = -13 + 2x 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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