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Simplifying ln(x2 + -4) = ln * 5 + 2ln * 3 Reorder the terms: ln(-4 + x2) = ln * 5 + 2ln * 3 (-4 * ln + x2 * ln) = ln * 5 + 2ln * 3 (-4ln + lnx2) = ln * 5 + 2ln * 3 Reorder the terms for easier multiplication: -4ln + lnx2 = 5ln + 2ln * 3 Reorder the terms for easier multiplication: -4ln + lnx2 = 5ln + 2 * 3ln Multiply 2 * 3 -4ln + lnx2 = 5ln + 6ln Combine like terms: 5ln + 6ln = 11ln -4ln + lnx2 = 11ln Solving -4ln + lnx2 = 11ln 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. -4ln + -11ln + lnx2 = 11ln + -11ln Combine like terms: -4ln + -11ln = -15ln -15ln + lnx2 = 11ln + -11ln Combine like terms: 11ln + -11ln = 0 -15ln + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + x2) = 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 '(-15 + x2)' equal to zero and attempt to solve: Simplifying -15 + x2 = 0 Solving -15 + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + x2 = 0 + 15 x2 = 0 + 15 Combine like terms: 0 + 15 = 15 x2 = 15 Add '-1x2' to each side of the equation. x2 + -1x2 = 15 + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 15 + -1x2 Simplifying 0 = 15 + -1x2 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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