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Simplifying ln(x + -8) + ln(x + 7) = ln(x + -57) Reorder the terms: ln(-8 + x) + ln(x + 7) = ln(x + -57) (-8 * ln + x * ln) + ln(x + 7) = ln(x + -57) (-8ln + lnx) + ln(x + 7) = ln(x + -57) Reorder the terms: -8ln + lnx + ln(7 + x) = ln(x + -57) -8ln + lnx + (7 * ln + x * ln) = ln(x + -57) -8ln + lnx + (7ln + lnx) = ln(x + -57) Reorder the terms: -8ln + 7ln + lnx + lnx = ln(x + -57) Combine like terms: -8ln + 7ln = -1ln -1ln + lnx + lnx = ln(x + -57) Combine like terms: lnx + lnx = 2lnx -1ln + 2lnx = ln(x + -57) Reorder the terms: -1ln + 2lnx = ln(-57 + x) -1ln + 2lnx = (-57 * ln + x * ln) -1ln + 2lnx = (-57ln + lnx) Solving -1ln + 2lnx = -57ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '57ln' to each side of the equation. -1ln + 57ln + 2lnx = -57ln + 57ln + lnx Combine like terms: -1ln + 57ln = 56ln 56ln + 2lnx = -57ln + 57ln + lnx Combine like terms: -57ln + 57ln = 0 56ln + 2lnx = 0 + lnx 56ln + 2lnx = lnx Add '-1lnx' to each side of the equation. 56ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx 56ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 56ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(56 + 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 '(56 + x)' equal to zero and attempt to solve: Simplifying 56 + x = 0 Solving 56 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-56' to each side of the equation. 56 + -56 + x = 0 + -56 Combine like terms: 56 + -56 = 0 0 + x = 0 + -56 x = 0 + -56 Combine like terms: 0 + -56 = -56 x = -56 Add '-1x' to each side of the equation. x + -1x = -56 + -1x Combine like terms: x + -1x = 0 0 = -56 + -1x Simplifying 0 = -56 + -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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