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Simplifying 50 = 10 + 5ln(3x + 6) Reorder the terms: 50 = 10 + 5ln(6 + 3x) 50 = 10 + (6 * 5ln + 3x * 5ln) 50 = 10 + (30ln + 15lnx) Solving 50 = 10 + 30ln + 15lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. 50 + -30ln = 10 + 30ln + -30ln + 15lnx Combine like terms: 30ln + -30ln = 0 50 + -30ln = 10 + 0 + 15lnx 50 + -30ln = 10 + 15lnx Add '-15lnx' to each side of the equation. 50 + -30ln + -15lnx = 10 + 15lnx + -15lnx Combine like terms: 15lnx + -15lnx = 0 50 + -30ln + -15lnx = 10 + 0 50 + -30ln + -15lnx = 10 Add '-50' to each side of the equation. 50 + -30ln + -50 + -15lnx = 10 + -50 Reorder the terms: 50 + -50 + -30ln + -15lnx = 10 + -50 Combine like terms: 50 + -50 = 0 0 + -30ln + -15lnx = 10 + -50 -30ln + -15lnx = 10 + -50 Combine like terms: 10 + -50 = -40 -30ln + -15lnx = -40 Reorder the terms: 40 + -30ln + -15lnx = -40 + 40 Combine like terms: -40 + 40 = 0 40 + -30ln + -15lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(8 + -6ln + -3lnx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8 + -6ln + -3lnx)' equal to zero and attempt to solve: Simplifying 8 + -6ln + -3lnx = 0 Solving 8 + -6ln + -3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -6ln + -8 + -3lnx = 0 + -8 Reorder the terms: 8 + -8 + -6ln + -3lnx = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -6ln + -3lnx = 0 + -8 -6ln + -3lnx = 0 + -8 Combine like terms: 0 + -8 = -8 -6ln + -3lnx = -8 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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