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Simplifying ln(5) = ln(x + 6) + -1ln(12) Reorder the terms for easier multiplication: 5ln = ln(x + 6) + -1ln(12) Reorder the terms: 5ln = ln(6 + x) + -1ln(12) 5ln = (6 * ln + x * ln) + -1ln(12) 5ln = (6ln + lnx) + -1ln(12) Reorder the terms for easier multiplication: 5ln = 6ln + lnx + -1 * 12ln Multiply -1 * 12 5ln = 6ln + lnx + -12ln Reorder the terms: 5ln = 6ln + -12ln + lnx Combine like terms: 6ln + -12ln = -6ln 5ln = -6ln + lnx Solving 5ln = -6ln + lnx 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. 5ln + 6ln = -6ln + 6ln + lnx Combine like terms: 5ln + 6ln = 11ln 11ln = -6ln + 6ln + lnx Combine like terms: -6ln + 6ln = 0 11ln = 0 + lnx 11ln = lnx Add '-1lnx' to each side of the equation. 11ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 11ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(11 + -1x) = 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 '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Add 'x' to each side of the equation. -1x + x = -11 + x Combine like terms: -1x + x = 0 0 = -11 + x Simplifying 0 = -11 + 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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