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Simplifying 48 = 12 + 6ln(2x + 1) Reorder the terms: 48 = 12 + 6ln(1 + 2x) 48 = 12 + (1 * 6ln + 2x * 6ln) 48 = 12 + (6ln + 12lnx) Solving 48 = 12 + 6ln + 12lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 48 + -6ln = 12 + 6ln + -6ln + 12lnx Combine like terms: 6ln + -6ln = 0 48 + -6ln = 12 + 0 + 12lnx 48 + -6ln = 12 + 12lnx Add '-12lnx' to each side of the equation. 48 + -6ln + -12lnx = 12 + 12lnx + -12lnx Combine like terms: 12lnx + -12lnx = 0 48 + -6ln + -12lnx = 12 + 0 48 + -6ln + -12lnx = 12 Add '-48' to each side of the equation. 48 + -6ln + -48 + -12lnx = 12 + -48 Reorder the terms: 48 + -48 + -6ln + -12lnx = 12 + -48 Combine like terms: 48 + -48 = 0 0 + -6ln + -12lnx = 12 + -48 -6ln + -12lnx = 12 + -48 Combine like terms: 12 + -48 = -36 -6ln + -12lnx = -36 Reorder the terms: 36 + -6ln + -12lnx = -36 + 36 Combine like terms: -36 + 36 = 0 36 + -6ln + -12lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(6 + -1ln + -2lnx) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(6 + -1ln + -2lnx)' equal to zero and attempt to solve: Simplifying 6 + -1ln + -2lnx = 0 Solving 6 + -1ln + -2lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -1ln + -6 + -2lnx = 0 + -6 Reorder the terms: 6 + -6 + -1ln + -2lnx = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1ln + -2lnx = 0 + -6 -1ln + -2lnx = 0 + -6 Combine like terms: 0 + -6 = -6 -1ln + -2lnx = -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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