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Simplifying 30 = 8ln(x + 4) Reorder the terms: 30 = 8ln(4 + x) 30 = (4 * 8ln + x * 8ln) 30 = (32ln + 8lnx) Solving 30 = 32ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32ln' to each side of the equation. 30 + -32ln = 32ln + -32ln + 8lnx Combine like terms: 32ln + -32ln = 0 30 + -32ln = 0 + 8lnx 30 + -32ln = 8lnx Add '-8lnx' to each side of the equation. 30 + -32ln + -8lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 30 + -32ln + -8lnx = 0 Add '-30' to each side of the equation. 30 + -32ln + -30 + -8lnx = 0 + -30 Reorder the terms: 30 + -30 + -32ln + -8lnx = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -32ln + -8lnx = 0 + -30 -32ln + -8lnx = 0 + -30 Combine like terms: 0 + -30 = -30 -32ln + -8lnx = -30 Reorder the terms: 30 + -32ln + -8lnx = -30 + 30 Combine like terms: -30 + 30 = 0 30 + -32ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -16ln + -4lnx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -16ln + -4lnx)' equal to zero and attempt to solve: Simplifying 15 + -16ln + -4lnx = 0 Solving 15 + -16ln + -4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -16ln + -15 + -4lnx = 0 + -15 Reorder the terms: 15 + -15 + -16ln + -4lnx = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -16ln + -4lnx = 0 + -15 -16ln + -4lnx = 0 + -15 Combine like terms: 0 + -15 = -15 -16ln + -4lnx = -15 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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