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Simplifying 2ln(4 + -3x) + 1 = 7 (4 * 2ln + -3x * 2ln) + 1 = 7 (8ln + -6lnx) + 1 = 7 Reorder the terms: 1 + 8ln + -6lnx = 7 Solving 1 + 8ln + -6lnx = 7 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 8ln + -1 + -6lnx = 7 + -1 Reorder the terms: 1 + -1 + 8ln + -6lnx = 7 + -1 Combine like terms: 1 + -1 = 0 0 + 8ln + -6lnx = 7 + -1 8ln + -6lnx = 7 + -1 Combine like terms: 7 + -1 = 6 8ln + -6lnx = 6 Reorder the terms: -6 + 8ln + -6lnx = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 8ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 4ln + -3lnx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 4ln + -3lnx)' equal to zero and attempt to solve: Simplifying -3 + 4ln + -3lnx = 0 Solving -3 + 4ln + -3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 4ln + 3 + -3lnx = 0 + 3 Reorder the terms: -3 + 3 + 4ln + -3lnx = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4ln + -3lnx = 0 + 3 4ln + -3lnx = 0 + 3 Combine like terms: 0 + 3 = 3 4ln + -3lnx = 3 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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