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Simplifying ln(x + -8) + ln(x + 5) = ln(7) Reorder the terms: ln(-8 + x) + ln(x + 5) = ln(7) (-8 * ln + x * ln) + ln(x + 5) = ln(7) (-8ln + lnx) + ln(x + 5) = ln(7) Reorder the terms: -8ln + lnx + ln(5 + x) = ln(7) -8ln + lnx + (5 * ln + x * ln) = ln(7) -8ln + lnx + (5ln + lnx) = ln(7) Reorder the terms: -8ln + 5ln + lnx + lnx = ln(7) Combine like terms: -8ln + 5ln = -3ln -3ln + lnx + lnx = ln(7) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(7) Reorder the terms for easier multiplication: -3ln + 2lnx = 7ln Solving -3ln + 2lnx = 7ln 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. -3ln + -7ln + 2lnx = 7ln + -7ln Combine like terms: -3ln + -7ln = -10ln -10ln + 2lnx = 7ln + -7ln Combine like terms: 7ln + -7ln = 0 -10ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-5 + x) = 0 Ignore the factor 2.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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -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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