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Simplifying lnx + -1ln(x + -6) = ln(11x + -72) Reorder the terms: lnx + -1ln(-6 + x) = ln(11x + -72) lnx + (-6 * -1ln + x * -1ln) = ln(11x + -72) lnx + (6ln + -1lnx) = ln(11x + -72) Reorder the terms: 6ln + lnx + -1lnx = ln(11x + -72) Combine like terms: lnx + -1lnx = 0 6ln + 0 = ln(11x + -72) 6ln = ln(11x + -72) Reorder the terms: 6ln = ln(-72 + 11x) 6ln = (-72 * ln + 11x * ln) 6ln = (-72ln + 11lnx) Solving 6ln = -72ln + 11lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '72ln' to each side of the equation. 6ln + 72ln = -72ln + 72ln + 11lnx Combine like terms: 6ln + 72ln = 78ln 78ln = -72ln + 72ln + 11lnx Combine like terms: -72ln + 72ln = 0 78ln = 0 + 11lnx 78ln = 11lnx Add '-11lnx' to each side of the equation. 78ln + -11lnx = 11lnx + -11lnx Combine like terms: 11lnx + -11lnx = 0 78ln + -11lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(78 + -11x) = 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 '(78 + -11x)' equal to zero and attempt to solve: Simplifying 78 + -11x = 0 Solving 78 + -11x = 0 Move all terms containing l to the left, all other terms to the right. Add '-78' to each side of the equation. 78 + -78 + -11x = 0 + -78 Combine like terms: 78 + -78 = 0 0 + -11x = 0 + -78 -11x = 0 + -78 Combine like terms: 0 + -78 = -78 -11x = -78 Add '11x' to each side of the equation. -11x + 11x = -78 + 11x Combine like terms: -11x + 11x = 0 0 = -78 + 11x Simplifying 0 = -78 + 11x 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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