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Simplifying ln(2x + 3) + -1ln(4x + 5) = 7 Reorder the terms: ln(3 + 2x) + -1ln(4x + 5) = 7 (3 * ln + 2x * ln) + -1ln(4x + 5) = 7 (3ln + 2lnx) + -1ln(4x + 5) = 7 Reorder the terms: 3ln + 2lnx + -1ln(5 + 4x) = 7 3ln + 2lnx + (5 * -1ln + 4x * -1ln) = 7 3ln + 2lnx + (-5ln + -4lnx) = 7 Reorder the terms: 3ln + -5ln + 2lnx + -4lnx = 7 Combine like terms: 3ln + -5ln = -2ln -2ln + 2lnx + -4lnx = 7 Combine like terms: 2lnx + -4lnx = -2lnx -2ln + -2lnx = 7 Solving -2ln + -2lnx = 7 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -7 + -2ln + -2lnx = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -2ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 2ln + 2lnx) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 2ln + 2lnx)' equal to zero and attempt to solve: Simplifying 7 + 2ln + 2lnx = 0 Solving 7 + 2ln + 2lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + 2ln + -7 + 2lnx = 0 + -7 Reorder the terms: 7 + -7 + 2ln + 2lnx = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2ln + 2lnx = 0 + -7 2ln + 2lnx = 0 + -7 Combine like terms: 0 + -7 = -7 2ln + 2lnx = -7 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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