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