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Simplifying 2ln(x) + -1ln(3x + -8) = ln(7x) + -1ln(x + 6) Multiply ln * x 2lnx + -1ln(3x + -8) = ln(7x) + -1ln(x + 6) Reorder the terms: 2lnx + -1ln(-8 + 3x) = ln(7x) + -1ln(x + 6) 2lnx + (-8 * -1ln + 3x * -1ln) = ln(7x) + -1ln(x + 6) 2lnx + (8ln + -3lnx) = ln(7x) + -1ln(x + 6) Reorder the terms: 8ln + 2lnx + -3lnx = ln(7x) + -1ln(x + 6) Combine like terms: 2lnx + -3lnx = -1lnx 8ln + -1lnx = ln(7x) + -1ln(x + 6) Remove parenthesis around (7x) 8ln + -1lnx = ln * 7x + -1ln(x + 6) Reorder the terms for easier multiplication: 8ln + -1lnx = 7ln * x + -1ln(x + 6) Multiply ln * x 8ln + -1lnx = 7lnx + -1ln(x + 6) Reorder the terms: 8ln + -1lnx = 7lnx + -1ln(6 + x) 8ln + -1lnx = 7lnx + (6 * -1ln + x * -1ln) 8ln + -1lnx = 7lnx + (-6ln + -1lnx) Reorder the terms: 8ln + -1lnx = -6ln + 7lnx + -1lnx Combine like terms: 7lnx + -1lnx = 6lnx 8ln + -1lnx = -6ln + 6lnx Solving 8ln + -1lnx = -6ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 8ln + 6ln + -1lnx = -6ln + 6ln + 6lnx Combine like terms: 8ln + 6ln = 14ln 14ln + -1lnx = -6ln + 6ln + 6lnx Combine like terms: -6ln + 6ln = 0 14ln + -1lnx = 0 + 6lnx 14ln + -1lnx = 6lnx Add '-6lnx' to each side of the equation. 14ln + -1lnx + -6lnx = 6lnx + -6lnx Combine like terms: -1lnx + -6lnx = -7lnx 14ln + -7lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 14ln + -7lnx = 0 Factor out the Greatest Common Factor (GCF), '7ln'. 7ln(2 + -1x) = 0 Ignore the factor 7.Subproblem 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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