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Simplifying 5ln(x + 9) + -6lnx = 0 Reorder the terms: 5ln(9 + x) + -6lnx = 0 (9 * 5ln + x * 5ln) + -6lnx = 0 (45ln + 5lnx) + -6lnx = 0 Combine like terms: 5lnx + -6lnx = -1lnx 45ln + -1lnx = 0 Solving 45ln + -1lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(45 + -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 '(45 + -1x)' equal to zero and attempt to solve: Simplifying 45 + -1x = 0 Solving 45 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + -1x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -1x = 0 + -45 -1x = 0 + -45 Combine like terms: 0 + -45 = -45 -1x = -45 Add 'x' to each side of the equation. -1x + x = -45 + x Combine like terms: -1x + x = 0 0 = -45 + x Simplifying 0 = -45 + 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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