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Simplifying 46 = 10 + 4ln(3x + 1) Reorder the terms: 46 = 10 + 4ln(1 + 3x) 46 = 10 + (1 * 4ln + 3x * 4ln) 46 = 10 + (4ln + 12lnx) Solving 46 = 10 + 4ln + 12lnx 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. 46 + -4ln = 10 + 4ln + -4ln + 12lnx Combine like terms: 4ln + -4ln = 0 46 + -4ln = 10 + 0 + 12lnx 46 + -4ln = 10 + 12lnx Add '-12lnx' to each side of the equation. 46 + -4ln + -12lnx = 10 + 12lnx + -12lnx Combine like terms: 12lnx + -12lnx = 0 46 + -4ln + -12lnx = 10 + 0 46 + -4ln + -12lnx = 10 Add '-46' to each side of the equation. 46 + -4ln + -46 + -12lnx = 10 + -46 Reorder the terms: 46 + -46 + -4ln + -12lnx = 10 + -46 Combine like terms: 46 + -46 = 0 0 + -4ln + -12lnx = 10 + -46 -4ln + -12lnx = 10 + -46 Combine like terms: 10 + -46 = -36 -4ln + -12lnx = -36 Reorder the terms: 36 + -4ln + -12lnx = -36 + 36 Combine like terms: -36 + 36 = 0 36 + -4ln + -12lnx = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -1ln + -3lnx) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -1ln + -3lnx)' equal to zero and attempt to solve: Simplifying 9 + -1ln + -3lnx = 0 Solving 9 + -1ln + -3lnx = 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 + -3lnx = 0 + -9 Reorder the terms: 9 + -9 + -1ln + -3lnx = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1ln + -3lnx = 0 + -9 -1ln + -3lnx = 0 + -9 Combine like terms: 0 + -9 = -9 -1ln + -3lnx = -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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