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