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Simplifying ln(6x + -11) = ln(3 + -4x) Reorder the terms: 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 = -14ln -14ln + 6lnx = 3ln + -3ln + -4lnx Combine like terms: 3ln + -3ln = 0 -14ln + 6lnx = 0 + -4lnx -14ln + 6lnx = -4lnx Add '4lnx' to each side of the equation. -14ln + 6lnx + 4lnx = -4lnx + 4lnx Combine like terms: 6lnx + 4lnx = 10lnx -14ln + 10lnx = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 -14ln + 10lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-7 + 5x) = 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 '(-7 + 5x)' equal to zero and attempt to solve: Simplifying -7 + 5x = 0 Solving -7 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 5x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5x = 0 + 7 5x = 0 + 7 Combine like terms: 0 + 7 = 7 5x = 7 Add '-5x' to each side of the equation. 5x + -5x = 7 + -5x Combine like terms: 5x + -5x = 0 0 = 7 + -5x Simplifying 0 = 7 + -5x 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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