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Simplifying ln(x + -1) + ln(x + -2) = ln(8x + 28) Reorder the terms: ln(-1 + x) + ln(x + -2) = ln(8x + 28) (-1 * ln + x * ln) + ln(x + -2) = ln(8x + 28) (-1ln + lnx) + ln(x + -2) = ln(8x + 28) Reorder the terms: -1ln + lnx + ln(-2 + x) = ln(8x + 28) -1ln + lnx + (-2 * ln + x * ln) = ln(8x + 28) -1ln + lnx + (-2ln + lnx) = ln(8x + 28) Reorder the terms: -1ln + -2ln + lnx + lnx = ln(8x + 28) Combine like terms: -1ln + -2ln = -3ln -3ln + lnx + lnx = ln(8x + 28) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(8x + 28) Reorder the terms: -3ln + 2lnx = ln(28 + 8x) -3ln + 2lnx = (28 * ln + 8x * ln) -3ln + 2lnx = (28ln + 8lnx) Solving -3ln + 2lnx = 28ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-28ln' to each side of the equation. -3ln + -28ln + 2lnx = 28ln + -28ln + 8lnx Combine like terms: -3ln + -28ln = -31ln -31ln + 2lnx = 28ln + -28ln + 8lnx Combine like terms: 28ln + -28ln = 0 -31ln + 2lnx = 0 + 8lnx -31ln + 2lnx = 8lnx Add '-8lnx' to each side of the equation. -31ln + 2lnx + -8lnx = 8lnx + -8lnx Combine like terms: 2lnx + -8lnx = -6lnx -31ln + -6lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 -31ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(31 + 6x) = 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 '(31 + 6x)' equal to zero and attempt to solve: Simplifying 31 + 6x = 0 Solving 31 + 6x = 0 Move all terms containing l to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + 6x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 6x = 0 + -31 6x = 0 + -31 Combine like terms: 0 + -31 = -31 6x = -31 Add '-6x' to each side of the equation. 6x + -6x = -31 + -6x Combine like terms: 6x + -6x = 0 0 = -31 + -6x Simplifying 0 = -31 + -6x 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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