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Simplifying ln(x + 1) + ln(x + -5) = ln(86) Reorder the terms: ln(1 + x) + ln(x + -5) = ln(86) (1 * ln + x * ln) + ln(x + -5) = ln(86) (1ln + lnx) + ln(x + -5) = ln(86) Reorder the terms: 1ln + lnx + ln(-5 + x) = ln(86) 1ln + lnx + (-5 * ln + x * ln) = ln(86) 1ln + lnx + (-5ln + lnx) = ln(86) Reorder the terms: 1ln + -5ln + lnx + lnx = ln(86) Combine like terms: 1ln + -5ln = -4ln -4ln + lnx + lnx = ln(86) Combine like terms: lnx + lnx = 2lnx -4ln + 2lnx = ln(86) Reorder the terms for easier multiplication: -4ln + 2lnx = 86ln Solving -4ln + 2lnx = 86ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-86ln' to each side of the equation. -4ln + -86ln + 2lnx = 86ln + -86ln Combine like terms: -4ln + -86ln = -90ln -90ln + 2lnx = 86ln + -86ln Combine like terms: 86ln + -86ln = 0 -90ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-45 + 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 '(-45 + x)' equal to zero and attempt to solve: Simplifying -45 + x = 0 Solving -45 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 0 + 45 Combine like terms: -45 + 45 = 0 0 + x = 0 + 45 x = 0 + 45 Combine like terms: 0 + 45 = 45 x = 45 Add '-1x' to each side of the equation. x + -1x = 45 + -1x Combine like terms: x + -1x = 0 0 = 45 + -1x Simplifying 0 = 45 + -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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