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Simplifying ln(11x) = ln(x2 + 24) Remove parenthesis around (11x) ln * 11x = ln(x2 + 24) Reorder the terms for easier multiplication: 11ln * x = ln(x2 + 24) Multiply ln * x 11lnx = ln(x2 + 24) Reorder the terms: 11lnx = ln(24 + x2) 11lnx = (24 * ln + x2 * ln) 11lnx = (24ln + lnx2) Solving 11lnx = 24ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. -24ln + 11lnx = 24ln + -24ln + lnx2 Combine like terms: 24ln + -24ln = 0 -24ln + 11lnx = 0 + lnx2 -24ln + 11lnx = lnx2 Add '-1lnx2' to each side of the equation. -24ln + 11lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -24ln + 11lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-24 + 11x + -1x2) = 0 Factor a trinomial. ln((-8 + x)(3 + -1x)) = 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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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