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Simplifying ln(8x + -11) + -1ln(3x + 4) = ln(x + -2) Reorder the terms: ln(-11 + 8x) + -1ln(3x + 4) = ln(x + -2) (-11 * ln + 8x * ln) + -1ln(3x + 4) = ln(x + -2) (-11ln + 8lnx) + -1ln(3x + 4) = ln(x + -2) Reorder the terms: -11ln + 8lnx + -1ln(4 + 3x) = ln(x + -2) -11ln + 8lnx + (4 * -1ln + 3x * -1ln) = ln(x + -2) -11ln + 8lnx + (-4ln + -3lnx) = ln(x + -2) Reorder the terms: -11ln + -4ln + 8lnx + -3lnx = ln(x + -2) Combine like terms: -11ln + -4ln = -15ln -15ln + 8lnx + -3lnx = ln(x + -2) Combine like terms: 8lnx + -3lnx = 5lnx -15ln + 5lnx = ln(x + -2) Reorder the terms: -15ln + 5lnx = ln(-2 + x) -15ln + 5lnx = (-2 * ln + x * ln) -15ln + 5lnx = (-2ln + lnx) Solving -15ln + 5lnx = -2ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. -15ln + 2ln + 5lnx = -2ln + 2ln + lnx Combine like terms: -15ln + 2ln = -13ln -13ln + 5lnx = -2ln + 2ln + lnx Combine like terms: -2ln + 2ln = 0 -13ln + 5lnx = 0 + lnx -13ln + 5lnx = lnx Add '-1lnx' to each side of the equation. -13ln + 5lnx + -1lnx = lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx -13ln + 4lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -13ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 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 '(-13 + 4x)' equal to zero and attempt to solve: Simplifying -13 + 4x = 0 Solving -13 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 4x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4x = 0 + 13 4x = 0 + 13 Combine like terms: 0 + 13 = 13 4x = 13 Add '-4x' to each side of the equation. 4x + -4x = 13 + -4x Combine like terms: 4x + -4x = 0 0 = 13 + -4x Simplifying 0 = 13 + -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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