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