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Simplifying 4ln(3x) + 8 = 2 + -4ln(2y) Remove parenthesis around (3x) 4ln * 3x + 8 = 2 + -4ln(2y) Reorder the terms for easier multiplication: 4 * 3ln * x + 8 = 2 + -4ln(2y) Multiply 4 * 3 12ln * x + 8 = 2 + -4ln(2y) Multiply ln * x 12lnx + 8 = 2 + -4ln(2y) Reorder the terms: 8 + 12lnx = 2 + -4ln(2y) Remove parenthesis around (2y) 8 + 12lnx = 2 + -4ln * 2y Reorder the terms for easier multiplication: 8 + 12lnx = 2 + -4 * 2ln * y Multiply -4 * 2 8 + 12lnx = 2 + -8ln * y Multiply ln * y 8 + 12lnx = 2 + -8lny Solving 8 + 12lnx = 2 + -8lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8lny' to each side of the equation. 8 + 12lnx + 8lny = 2 + -8lny + 8lny Combine like terms: -8lny + 8lny = 0 8 + 12lnx + 8lny = 2 + 0 8 + 12lnx + 8lny = 2 Add '-8' to each side of the equation. 8 + 12lnx + -8 + 8lny = 2 + -8 Reorder the terms: 8 + -8 + 12lnx + 8lny = 2 + -8 Combine like terms: 8 + -8 = 0 0 + 12lnx + 8lny = 2 + -8 12lnx + 8lny = 2 + -8 Combine like terms: 2 + -8 = -6 12lnx + 8lny = -6 Reorder the terms: 6 + 12lnx + 8lny = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 12lnx + 8lny = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 6lnx + 4lny) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 6lnx + 4lny)' equal to zero and attempt to solve: Simplifying 3 + 6lnx + 4lny = 0 Solving 3 + 6lnx + 4lny = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 6lnx + -3 + 4lny = 0 + -3 Reorder the terms: 3 + -3 + 6lnx + 4lny = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 6lnx + 4lny = 0 + -3 6lnx + 4lny = 0 + -3 Combine like terms: 0 + -3 = -3 6lnx + 4lny = -3 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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