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Simplifying 18 = 3ln(x + 5) Reorder the terms: 18 = 3ln(5 + x) 18 = (5 * 3ln + x * 3ln) 18 = (15ln + 3lnx) Solving 18 = 15ln + 3lnx 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. 18 + -15ln = 15ln + -15ln + 3lnx Combine like terms: 15ln + -15ln = 0 18 + -15ln = 0 + 3lnx 18 + -15ln = 3lnx Add '-3lnx' to each side of the equation. 18 + -15ln + -3lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 18 + -15ln + -3lnx = 0 Add '-18' to each side of the equation. 18 + -15ln + -18 + -3lnx = 0 + -18 Reorder the terms: 18 + -18 + -15ln + -3lnx = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -15ln + -3lnx = 0 + -18 -15ln + -3lnx = 0 + -18 Combine like terms: 0 + -18 = -18 -15ln + -3lnx = -18 Reorder the terms: 18 + -15ln + -3lnx = -18 + 18 Combine like terms: -18 + 18 = 0 18 + -15ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -5ln + -1lnx) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -5ln + -1lnx)' equal to zero and attempt to solve: Simplifying 6 + -5ln + -1lnx = 0 Solving 6 + -5ln + -1lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -5ln + -6 + -1lnx = 0 + -6 Reorder the terms: 6 + -6 + -5ln + -1lnx = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5ln + -1lnx = 0 + -6 -5ln + -1lnx = 0 + -6 Combine like terms: 0 + -6 = -6 -5ln + -1lnx = -6 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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