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Simplifying 2ln(x) + -1ln(2x + -5) = ln(7x) + -1ln(x + 2) Multiply ln * x 2lnx + -1ln(2x + -5) = ln(7x) + -1ln(x + 2) Reorder the terms: 2lnx + -1ln(-5 + 2x) = ln(7x) + -1ln(x + 2) 2lnx + (-5 * -1ln + 2x * -1ln) = ln(7x) + -1ln(x + 2) 2lnx + (5ln + -2lnx) = ln(7x) + -1ln(x + 2) Reorder the terms: 5ln + 2lnx + -2lnx = ln(7x) + -1ln(x + 2) Combine like terms: 2lnx + -2lnx = 0 5ln + 0 = ln(7x) + -1ln(x + 2) 5ln = ln(7x) + -1ln(x + 2) Remove parenthesis around (7x) 5ln = ln * 7x + -1ln(x + 2) Reorder the terms for easier multiplication: 5ln = 7ln * x + -1ln(x + 2) Multiply ln * x 5ln = 7lnx + -1ln(x + 2) Reorder the terms: 5ln = 7lnx + -1ln(2 + x) 5ln = 7lnx + (2 * -1ln + x * -1ln) 5ln = 7lnx + (-2ln + -1lnx) Reorder the terms: 5ln = -2ln + 7lnx + -1lnx Combine like terms: 7lnx + -1lnx = 6lnx 5ln = -2ln + 6lnx Solving 5ln = -2ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 5ln + 2ln = -2ln + 2ln + 6lnx Combine like terms: 5ln + 2ln = 7ln 7ln = -2ln + 2ln + 6lnx Combine like terms: -2ln + 2ln = 0 7ln = 0 + 6lnx 7ln = 6lnx Add '-6lnx' to each side of the equation. 7ln + -6lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 7ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -6x) = 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 + -6x)' equal to zero and attempt to solve: Simplifying 7 + -6x = 0 Solving 7 + -6x = 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 + -6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x = 0 + -7 -6x = 0 + -7 Combine like terms: 0 + -7 = -7 -6x = -7 Add '6x' to each side of the equation. -6x + 6x = -7 + 6x Combine like terms: -6x + 6x = 0 0 = -7 + 6x Simplifying 0 = -7 + 6x 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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