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Simplifying ln(x + -2) + ln(x + 5) + -1ln(x2 + -7) = 0 Reorder the terms: ln(-2 + x) + ln(x + 5) + -1ln(x2 + -7) = 0 (-2 * ln + x * ln) + ln(x + 5) + -1ln(x2 + -7) = 0 (-2ln + lnx) + ln(x + 5) + -1ln(x2 + -7) = 0 Reorder the terms: -2ln + lnx + ln(5 + x) + -1ln(x2 + -7) = 0 -2ln + lnx + (5 * ln + x * ln) + -1ln(x2 + -7) = 0 -2ln + lnx + (5ln + lnx) + -1ln(x2 + -7) = 0 Reorder the terms: -2ln + lnx + 5ln + lnx + -1ln(-7 + x2) = 0 -2ln + lnx + 5ln + lnx + (-7 * -1ln + x2 * -1ln) = 0 -2ln + lnx + 5ln + lnx + (7ln + -1lnx2) = 0 Reorder the terms: -2ln + 5ln + 7ln + lnx + lnx + -1lnx2 = 0 Combine like terms: -2ln + 5ln = 3ln 3ln + 7ln + lnx + lnx + -1lnx2 = 0 Combine like terms: 3ln + 7ln = 10ln 10ln + lnx + lnx + -1lnx2 = 0 Combine like terms: lnx + lnx = 2lnx 10ln + 2lnx + -1lnx2 = 0 Solving 10ln + 2lnx + -1lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + 2x + -1x2) = 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 '(10 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 10 + 2x + -1x2 = 0 Solving 10 + 2x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + 2x + -10 + -1x2 = 0 + -10 Reorder the terms: 10 + -10 + 2x + -1x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 2x + -1x2 = 0 + -10 2x + -1x2 = 0 + -10 Combine like terms: 0 + -10 = -10 2x + -1x2 = -10 Add '-2x' to each side of the equation. 2x + -2x + -1x2 = -10 + -2x Combine like terms: 2x + -2x = 0 0 + -1x2 = -10 + -2x -1x2 = -10 + -2x Add 'x2' to each side of the equation. -1x2 + x2 = -10 + -2x + x2 Combine like terms: -1x2 + x2 = 0 0 = -10 + -2x + x2 Simplifying 0 = -10 + -2x + x2 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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