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