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Simplifying 48 = 12 + 4ln(2x + 1) Reorder the terms: 48 = 12 + 4ln(1 + 2x) 48 = 12 + (1 * 4ln + 2x * 4ln) 48 = 12 + (4ln + 8lnx) Solving 48 = 12 + 4ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 48 + -4ln = 12 + 4ln + -4ln + 8lnx Combine like terms: 4ln + -4ln = 0 48 + -4ln = 12 + 0 + 8lnx 48 + -4ln = 12 + 8lnx Add '-8lnx' to each side of the equation. 48 + -4ln + -8lnx = 12 + 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 48 + -4ln + -8lnx = 12 + 0 48 + -4ln + -8lnx = 12 Add '-48' to each side of the equation. 48 + -4ln + -48 + -8lnx = 12 + -48 Reorder the terms: 48 + -48 + -4ln + -8lnx = 12 + -48 Combine like terms: 48 + -48 = 0 0 + -4ln + -8lnx = 12 + -48 -4ln + -8lnx = 12 + -48 Combine like terms: 12 + -48 = -36 -4ln + -8lnx = -36 Reorder the terms: 36 + -4ln + -8lnx = -36 + 36 Combine like terms: -36 + 36 = 0 36 + -4ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -1ln + -2lnx) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -1ln + -2lnx)' equal to zero and attempt to solve: Simplifying 9 + -1ln + -2lnx = 0 Solving 9 + -1ln + -2lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -1ln + -9 + -2lnx = 0 + -9 Reorder the terms: 9 + -9 + -1ln + -2lnx = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1ln + -2lnx = 0 + -9 -1ln + -2lnx = 0 + -9 Combine like terms: 0 + -9 = -9 -1ln + -2lnx = -9 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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