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Simplifying 9 = 3ln(9x + 5) Reorder the terms: 9 = 3ln(5 + 9x) 9 = (5 * 3ln + 9x * 3ln) 9 = (15ln + 27lnx) Solving 9 = 15ln + 27lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 9 + -15ln = 15ln + -15ln + 27lnx Combine like terms: 15ln + -15ln = 0 9 + -15ln = 0 + 27lnx 9 + -15ln = 27lnx Add '-27lnx' to each side of the equation. 9 + -15ln + -27lnx = 27lnx + -27lnx Combine like terms: 27lnx + -27lnx = 0 9 + -15ln + -27lnx = 0 Add '-9' to each side of the equation. 9 + -15ln + -9 + -27lnx = 0 + -9 Reorder the terms: 9 + -9 + -15ln + -27lnx = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -15ln + -27lnx = 0 + -9 -15ln + -27lnx = 0 + -9 Combine like terms: 0 + -9 = -9 -15ln + -27lnx = -9 Reorder the terms: 9 + -15ln + -27lnx = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -15ln + -27lnx = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -5ln + -9lnx) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -5ln + -9lnx)' equal to zero and attempt to solve: Simplifying 3 + -5ln + -9lnx = 0 Solving 3 + -5ln + -9lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -5ln + -3 + -9lnx = 0 + -3 Reorder the terms: 3 + -3 + -5ln + -9lnx = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5ln + -9lnx = 0 + -3 -5ln + -9lnx = 0 + -3 Combine like terms: 0 + -3 = -3 -5ln + -9lnx = -3 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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