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Simplifying 32 = 16 + 4ln(4x + 3) Reorder the terms: 32 = 16 + 4ln(3 + 4x) 32 = 16 + (3 * 4ln + 4x * 4ln) 32 = 16 + (12ln + 16lnx) Solving 32 = 16 + 12ln + 16lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 32 + -12ln = 16 + 12ln + -12ln + 16lnx Combine like terms: 12ln + -12ln = 0 32 + -12ln = 16 + 0 + 16lnx 32 + -12ln = 16 + 16lnx Add '-16lnx' to each side of the equation. 32 + -12ln + -16lnx = 16 + 16lnx + -16lnx Combine like terms: 16lnx + -16lnx = 0 32 + -12ln + -16lnx = 16 + 0 32 + -12ln + -16lnx = 16 Add '-32' to each side of the equation. 32 + -12ln + -32 + -16lnx = 16 + -32 Reorder the terms: 32 + -32 + -12ln + -16lnx = 16 + -32 Combine like terms: 32 + -32 = 0 0 + -12ln + -16lnx = 16 + -32 -12ln + -16lnx = 16 + -32 Combine like terms: 16 + -32 = -16 -12ln + -16lnx = -16 Reorder the terms: 16 + -12ln + -16lnx = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -12ln + -16lnx = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -3ln + -4lnx) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -3ln + -4lnx)' equal to zero and attempt to solve: Simplifying 4 + -3ln + -4lnx = 0 Solving 4 + -3ln + -4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -3ln + -4 + -4lnx = 0 + -4 Reorder the terms: 4 + -4 + -3ln + -4lnx = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3ln + -4lnx = 0 + -4 -3ln + -4lnx = 0 + -4 Combine like terms: 0 + -4 = -4 -3ln + -4lnx = -4 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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