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Simplifying 40 = 10 + 5ln(3x + 7) Reorder the terms: 40 = 10 + 5ln(7 + 3x) 40 = 10 + (7 * 5ln + 3x * 5ln) 40 = 10 + (35ln + 15lnx) Solving 40 = 10 + 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. 40 + -35ln = 10 + 35ln + -35ln + 15lnx Combine like terms: 35ln + -35ln = 0 40 + -35ln = 10 + 0 + 15lnx 40 + -35ln = 10 + 15lnx Add '-15lnx' to each side of the equation. 40 + -35ln + -15lnx = 10 + 15lnx + -15lnx Combine like terms: 15lnx + -15lnx = 0 40 + -35ln + -15lnx = 10 + 0 40 + -35ln + -15lnx = 10 Add '-40' to each side of the equation. 40 + -35ln + -40 + -15lnx = 10 + -40 Reorder the terms: 40 + -40 + -35ln + -15lnx = 10 + -40 Combine like terms: 40 + -40 = 0 0 + -35ln + -15lnx = 10 + -40 -35ln + -15lnx = 10 + -40 Combine like terms: 10 + -40 = -30 -35ln + -15lnx = -30 Reorder the terms: 30 + -35ln + -15lnx = -30 + 30 Combine like terms: -30 + 30 = 0 30 + -35ln + -15lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(6 + -7ln + -3lnx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + -7ln + -3lnx)' equal to zero and attempt to solve: Simplifying 6 + -7ln + -3lnx = 0 Solving 6 + -7ln + -3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -7ln + -6 + -3lnx = 0 + -6 Reorder the terms: 6 + -6 + -7ln + -3lnx = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7ln + -3lnx = 0 + -6 -7ln + -3lnx = 0 + -6 Combine like terms: 0 + -6 = -6 -7ln + -3lnx = -6 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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