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