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Simplifying ln(11 + -6x) = ln(3 + -4x) (11 * ln + -6x * ln) = ln(3 + -4x) (11ln + -6lnx) = ln(3 + -4x) 11ln + -6lnx = (3 * ln + -4x * ln) 11ln + -6lnx = (3ln + -4lnx) Solving 11ln + -6lnx = 3ln + -4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 11ln + -3ln + -6lnx = 3ln + -3ln + -4lnx Combine like terms: 11ln + -3ln = 8ln 8ln + -6lnx = 3ln + -3ln + -4lnx Combine like terms: 3ln + -3ln = 0 8ln + -6lnx = 0 + -4lnx 8ln + -6lnx = -4lnx Add '4lnx' to each side of the equation. 8ln + -6lnx + 4lnx = -4lnx + 4lnx Combine like terms: -6lnx + 4lnx = -2lnx 8ln + -2lnx = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 8ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(4 + -1x) = 0 Ignore the factor 2.Subproblem 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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