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