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Simplifying ln(x + -4) * ln(x + 6) = lne5 Reorder the terms: ln(-4 + x) * ln(x + 6) = lne5 Reorder the terms: ln(-4 + x) * ln(6 + x) = lne5 Reorder the terms for easier multiplication: ln * ln(-4 + x)(6 + x) = lne5 Multiply ln * ln l2n2(-4 + x)(6 + x) = lne5 Multiply (-4 + x) * (6 + x) l2n2(-4(6 + x) + x(6 + x)) = lne5 l2n2((6 * -4 + x * -4) + x(6 + x)) = lne5 l2n2((-24 + -4x) + x(6 + x)) = lne5 l2n2(-24 + -4x + (6 * x + x * x)) = lne5 l2n2(-24 + -4x + (6x + x2)) = lne5 Combine like terms: -4x + 6x = 2x l2n2(-24 + 2x + x2) = lne5 (-24 * l2n2 + 2x * l2n2 + x2 * l2n2) = lne5 (-24l2n2 + 2l2n2x + l2n2x2) = lne5 Solving -24l2n2 + 2l2n2x + l2n2x2 = e5ln Solving for variable 'l'. Reorder the terms: -1e5ln + -24l2n2 + 2l2n2x + l2n2x2 = e5ln + -1e5ln Combine like terms: e5ln + -1e5ln = 0 -1e5ln + -24l2n2 + 2l2n2x + l2n2x2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1e5 + -24ln + 2lnx + lnx2) = 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 '(-1e5 + -24ln + 2lnx + lnx2)' equal to zero and attempt to solve: Simplifying -1e5 + -24ln + 2lnx + lnx2 = 0 Solving -1e5 + -24ln + 2lnx + lnx2 = 0 Move all terms containing l to the left, all other terms to the right. Add 'e5' to each side of the equation. -1e5 + -24ln + 2lnx + e5 + lnx2 = 0 + e5 Reorder the terms: -1e5 + e5 + -24ln + 2lnx + lnx2 = 0 + e5 Combine like terms: -1e5 + e5 = 0 0 + -24ln + 2lnx + lnx2 = 0 + e5 -24ln + 2lnx + lnx2 = 0 + e5 Remove the zero: -24ln + 2lnx + lnx2 = e5 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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