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Simplifying ln(6x + 11) = ln(5x + 6) Reorder the terms: ln(11 + 6x) = ln(5x + 6) (11 * ln + 6x * ln) = ln(5x + 6) (11ln + 6lnx) = ln(5x + 6) Reorder the terms: 11ln + 6lnx = ln(6 + 5x) 11ln + 6lnx = (6 * ln + 5x * ln) 11ln + 6lnx = (6ln + 5lnx) Solving 11ln + 6lnx = 6ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 11ln + -6ln + 6lnx = 6ln + -6ln + 5lnx Combine like terms: 11ln + -6ln = 5ln 5ln + 6lnx = 6ln + -6ln + 5lnx Combine like terms: 6ln + -6ln = 0 5ln + 6lnx = 0 + 5lnx 5ln + 6lnx = 5lnx Add '-5lnx' to each side of the equation. 5ln + 6lnx + -5lnx = 5lnx + -5lnx Combine like terms: 6lnx + -5lnx = 1lnx 5ln + 1lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 5ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + x) = 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -1x 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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