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Simplifying ln(x + 2) + ln(x + -1) = ln(9x + -17) Reorder the terms: ln(2 + x) + ln(x + -1) = ln(9x + -17) (2 * ln + x * ln) + ln(x + -1) = ln(9x + -17) (2ln + lnx) + ln(x + -1) = ln(9x + -17) Reorder the terms: 2ln + lnx + ln(-1 + x) = ln(9x + -17) 2ln + lnx + (-1 * ln + x * ln) = ln(9x + -17) 2ln + lnx + (-1ln + lnx) = ln(9x + -17) Reorder the terms: 2ln + -1ln + lnx + lnx = ln(9x + -17) Combine like terms: 2ln + -1ln = 1ln 1ln + lnx + lnx = ln(9x + -17) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(9x + -17) Reorder the terms: 1ln + 2lnx = ln(-17 + 9x) 1ln + 2lnx = (-17 * ln + 9x * ln) 1ln + 2lnx = (-17ln + 9lnx) Solving 1ln + 2lnx = -17ln + 9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '17ln' to each side of the equation. 1ln + 17ln + 2lnx = -17ln + 17ln + 9lnx Combine like terms: 1ln + 17ln = 18ln 18ln + 2lnx = -17ln + 17ln + 9lnx Combine like terms: -17ln + 17ln = 0 18ln + 2lnx = 0 + 9lnx 18ln + 2lnx = 9lnx Add '-9lnx' to each side of the equation. 18ln + 2lnx + -9lnx = 9lnx + -9lnx Combine like terms: 2lnx + -9lnx = -7lnx 18ln + -7lnx = 9lnx + -9lnx Combine like terms: 9lnx + -9lnx = 0 18ln + -7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(18 + -7x) = 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 '(18 + -7x)' equal to zero and attempt to solve: Simplifying 18 + -7x = 0 Solving 18 + -7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -7x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -7x = 0 + -18 -7x = 0 + -18 Combine like terms: 0 + -18 = -18 -7x = -18 Add '7x' to each side of the equation. -7x + 7x = -18 + 7x Combine like terms: -7x + 7x = 0 0 = -18 + 7x Simplifying 0 = -18 + 7x 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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