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Simplifying ln(x + -3) + ln(x + 1) = ln(x + 7) Reorder the terms: ln(-3 + x) + ln(x + 1) = ln(x + 7) (-3 * ln + x * ln) + ln(x + 1) = ln(x + 7) (-3ln + lnx) + ln(x + 1) = ln(x + 7) Reorder the terms: -3ln + lnx + ln(1 + x) = ln(x + 7) -3ln + lnx + (1 * ln + x * ln) = ln(x + 7) -3ln + lnx + (1ln + lnx) = ln(x + 7) Reorder the terms: -3ln + 1ln + lnx + lnx = ln(x + 7) Combine like terms: -3ln + 1ln = -2ln -2ln + lnx + lnx = ln(x + 7) Combine like terms: lnx + lnx = 2lnx -2ln + 2lnx = ln(x + 7) Reorder the terms: -2ln + 2lnx = ln(7 + x) -2ln + 2lnx = (7 * ln + x * ln) -2ln + 2lnx = (7ln + lnx) Solving -2ln + 2lnx = 7ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. -2ln + -7ln + 2lnx = 7ln + -7ln + lnx Combine like terms: -2ln + -7ln = -9ln -9ln + 2lnx = 7ln + -7ln + lnx Combine like terms: 7ln + -7ln = 0 -9ln + 2lnx = 0 + lnx -9ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -9ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -9ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -9ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + x) = 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Add '-1x' to each side of the equation. x + -1x = 9 + -1x Combine like terms: x + -1x = 0 0 = 9 + -1x Simplifying 0 = 9 + -1x 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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