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Simplifying 55 = 10 + 5ln(3x + 1) Reorder the terms: 55 = 10 + 5ln(1 + 3x) 55 = 10 + (1 * 5ln + 3x * 5ln) 55 = 10 + (5ln + 15lnx) Solving 55 = 10 + 5ln + 15lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 55 + -5ln = 10 + 5ln + -5ln + 15lnx Combine like terms: 5ln + -5ln = 0 55 + -5ln = 10 + 0 + 15lnx 55 + -5ln = 10 + 15lnx Add '-15lnx' to each side of the equation. 55 + -5ln + -15lnx = 10 + 15lnx + -15lnx Combine like terms: 15lnx + -15lnx = 0 55 + -5ln + -15lnx = 10 + 0 55 + -5ln + -15lnx = 10 Add '-55' to each side of the equation. 55 + -5ln + -55 + -15lnx = 10 + -55 Reorder the terms: 55 + -55 + -5ln + -15lnx = 10 + -55 Combine like terms: 55 + -55 = 0 0 + -5ln + -15lnx = 10 + -55 -5ln + -15lnx = 10 + -55 Combine like terms: 10 + -55 = -45 -5ln + -15lnx = -45 Reorder the terms: 45 + -5ln + -15lnx = -45 + 45 Combine like terms: -45 + 45 = 0 45 + -5ln + -15lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(9 + -1ln + -3lnx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(9 + -1ln + -3lnx)' equal to zero and attempt to solve: Simplifying 9 + -1ln + -3lnx = 0 Solving 9 + -1ln + -3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -1ln + -9 + -3lnx = 0 + -9 Reorder the terms: 9 + -9 + -1ln + -3lnx = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1ln + -3lnx = 0 + -9 -1ln + -3lnx = 0 + -9 Combine like terms: 0 + -9 = -9 -1ln + -3lnx = -9 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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