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Simplifying ln(x + 6) = ln(9x + -5) Reorder the terms: ln(6 + x) = ln(9x + -5) (6 * ln + x * ln) = ln(9x + -5) (6ln + lnx) = ln(9x + -5) Reorder the terms: 6ln + lnx = ln(-5 + 9x) 6ln + lnx = (-5 * ln + 9x * ln) 6ln + lnx = (-5ln + 9lnx) Solving 6ln + lnx = -5ln + 9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 6ln + 5ln + lnx = -5ln + 5ln + 9lnx Combine like terms: 6ln + 5ln = 11ln 11ln + lnx = -5ln + 5ln + 9lnx Combine like terms: -5ln + 5ln = 0 11ln + lnx = 0 + 9lnx 11ln + lnx = 9lnx Add '-9lnx' to each side of the equation. 11ln + lnx + -9lnx = 9lnx + -9lnx Combine like terms: lnx + -9lnx = -8lnx 11ln + -8lnx = 9lnx + -9lnx Combine like terms: 9lnx + -9lnx = 0 11ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(11 + -8x) = 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 + -8x)' equal to zero and attempt to solve: Simplifying 11 + -8x = 0 Solving 11 + -8x = 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 + -8x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8x = 0 + -11 -8x = 0 + -11 Combine like terms: 0 + -11 = -11 -8x = -11 Add '8x' to each side of the equation. -8x + 8x = -11 + 8x Combine like terms: -8x + 8x = 0 0 = -11 + 8x Simplifying 0 = -11 + 8x 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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