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Simplifying 7 + 6ln(3x + -2) = 13 Reorder the terms: 7 + 6ln(-2 + 3x) = 13 7 + (-2 * 6ln + 3x * 6ln) = 13 7 + (-12ln + 18lnx) = 13 Solving 7 + -12ln + 18lnx = 13 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -12ln + -7 + 18lnx = 13 + -7 Reorder the terms: 7 + -7 + -12ln + 18lnx = 13 + -7 Combine like terms: 7 + -7 = 0 0 + -12ln + 18lnx = 13 + -7 -12ln + 18lnx = 13 + -7 Combine like terms: 13 + -7 = 6 -12ln + 18lnx = 6 Reorder the terms: -6 + -12ln + 18lnx = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -12ln + 18lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-1 + -2ln + 3lnx) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -2ln + 3lnx)' equal to zero and attempt to solve: Simplifying -1 + -2ln + 3lnx = 0 Solving -1 + -2ln + 3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -2ln + 1 + 3lnx = 0 + 1 Reorder the terms: -1 + 1 + -2ln + 3lnx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2ln + 3lnx = 0 + 1 -2ln + 3lnx = 0 + 1 Combine like terms: 0 + 1 = 1 -2ln + 3lnx = 1 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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