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Simplifying 6ln(3x + 4) + 2 = 14 Reorder the terms: 6ln(4 + 3x) + 2 = 14 (4 * 6ln + 3x * 6ln) + 2 = 14 (24ln + 18lnx) + 2 = 14 Reorder the terms: 2 + 24ln + 18lnx = 14 Solving 2 + 24ln + 18lnx = 14 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 24ln + -2 + 18lnx = 14 + -2 Reorder the terms: 2 + -2 + 24ln + 18lnx = 14 + -2 Combine like terms: 2 + -2 = 0 0 + 24ln + 18lnx = 14 + -2 24ln + 18lnx = 14 + -2 Combine like terms: 14 + -2 = 12 24ln + 18lnx = 12 Reorder the terms: -12 + 24ln + 18lnx = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 24ln + 18lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + 4ln + 3lnx) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + 4ln + 3lnx)' equal to zero and attempt to solve: Simplifying -2 + 4ln + 3lnx = 0 Solving -2 + 4ln + 3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 4ln + 2 + 3lnx = 0 + 2 Reorder the terms: -2 + 2 + 4ln + 3lnx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4ln + 3lnx = 0 + 2 4ln + 3lnx = 0 + 2 Combine like terms: 0 + 2 = 2 4ln + 3lnx = 2 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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