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Simplifying 2ln(x + -2) + ln(3x + 1) = 2ln * 2 Reorder the terms: 2ln(-2 + x) + ln(3x + 1) = 2ln * 2 (-2 * 2ln + x * 2ln) + ln(3x + 1) = 2ln * 2 (-4ln + 2lnx) + ln(3x + 1) = 2ln * 2 Reorder the terms: -4ln + 2lnx + ln(1 + 3x) = 2ln * 2 -4ln + 2lnx + (1 * ln + 3x * ln) = 2ln * 2 -4ln + 2lnx + (1ln + 3lnx) = 2ln * 2 Reorder the terms: -4ln + 1ln + 2lnx + 3lnx = 2ln * 2 Combine like terms: -4ln + 1ln = -3ln -3ln + 2lnx + 3lnx = 2ln * 2 Combine like terms: 2lnx + 3lnx = 5lnx -3ln + 5lnx = 2ln * 2 Reorder the terms for easier multiplication: -3ln + 5lnx = 2 * 2ln Multiply 2 * 2 -3ln + 5lnx = 4ln Solving -3ln + 5lnx = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. -3ln + -4ln + 5lnx = 4ln + -4ln Combine like terms: -3ln + -4ln = -7ln -7ln + 5lnx = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -7ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + 5x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-7 + 5x)' equal to zero and attempt to solve: Simplifying -7 + 5x = 0 Solving -7 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 5x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5x = 0 + 7 5x = 0 + 7 Combine like terms: 0 + 7 = 7 5x = 7 Add '-5x' to each side of the equation. 5x + -5x = 7 + -5x Combine like terms: 5x + -5x = 0 0 = 7 + -5x Simplifying 0 = 7 + -5x 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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