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Simplifying 50 = 5ln(3x + 7) Reorder the terms: 50 = 5ln(7 + 3x) 50 = (7 * 5ln + 3x * 5ln) 50 = (35ln + 15lnx) Solving 50 = 35ln + 15lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-35ln' to each side of the equation. 50 + -35ln = 35ln + -35ln + 15lnx Combine like terms: 35ln + -35ln = 0 50 + -35ln = 0 + 15lnx 50 + -35ln = 15lnx Add '-15lnx' to each side of the equation. 50 + -35ln + -15lnx = 15lnx + -15lnx Combine like terms: 15lnx + -15lnx = 0 50 + -35ln + -15lnx = 0 Add '-50' to each side of the equation. 50 + -35ln + -50 + -15lnx = 0 + -50 Reorder the terms: 50 + -50 + -35ln + -15lnx = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -35ln + -15lnx = 0 + -50 -35ln + -15lnx = 0 + -50 Combine like terms: 0 + -50 = -50 -35ln + -15lnx = -50 Reorder the terms: 50 + -35ln + -15lnx = -50 + 50 Combine like terms: -50 + 50 = 0 50 + -35ln + -15lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(10 + -7ln + -3lnx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + -7ln + -3lnx)' equal to zero and attempt to solve: Simplifying 10 + -7ln + -3lnx = 0 Solving 10 + -7ln + -3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -7ln + -10 + -3lnx = 0 + -10 Reorder the terms: 10 + -10 + -7ln + -3lnx = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7ln + -3lnx = 0 + -10 -7ln + -3lnx = 0 + -10 Combine like terms: 0 + -10 = -10 -7ln + -3lnx = -10 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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