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Simplifying ln(11 + -6x) = ln(1 + -1x) (11 * ln + -6x * ln) = ln(1 + -1x) (11ln + -6lnx) = ln(1 + -1x) 11ln + -6lnx = (1 * ln + -1x * ln) 11ln + -6lnx = (1ln + -1lnx) Solving 11ln + -6lnx = 1ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 11ln + -1ln + -6lnx = 1ln + -1ln + -1lnx Combine like terms: 11ln + -1ln = 10ln 10ln + -6lnx = 1ln + -1ln + -1lnx Combine like terms: 1ln + -1ln = 0 10ln + -6lnx = 0 + -1lnx 10ln + -6lnx = -1lnx Add 'lnx' to each side of the equation. 10ln + -6lnx + lnx = -1lnx + lnx Combine like terms: -6lnx + lnx = -5lnx 10ln + -5lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 10ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), '5ln'. 5ln(2 + -1x) = 0 Ignore the factor 5.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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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