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Simplifying ln(x + 5) + ln(x + -1) = ln(22 + -2x) Reorder the terms: ln(5 + x) + ln(x + -1) = ln(22 + -2x) (5 * ln + x * ln) + ln(x + -1) = ln(22 + -2x) (5ln + lnx) + ln(x + -1) = ln(22 + -2x) Reorder the terms: 5ln + lnx + ln(-1 + x) = ln(22 + -2x) 5ln + lnx + (-1 * ln + x * ln) = ln(22 + -2x) 5ln + lnx + (-1ln + lnx) = ln(22 + -2x) Reorder the terms: 5ln + -1ln + lnx + lnx = ln(22 + -2x) Combine like terms: 5ln + -1ln = 4ln 4ln + lnx + lnx = ln(22 + -2x) Combine like terms: lnx + lnx = 2lnx 4ln + 2lnx = ln(22 + -2x) 4ln + 2lnx = (22 * ln + -2x * ln) 4ln + 2lnx = (22ln + -2lnx) Solving 4ln + 2lnx = 22ln + -2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-22ln' to each side of the equation. 4ln + -22ln + 2lnx = 22ln + -22ln + -2lnx Combine like terms: 4ln + -22ln = -18ln -18ln + 2lnx = 22ln + -22ln + -2lnx Combine like terms: 22ln + -22ln = 0 -18ln + 2lnx = 0 + -2lnx -18ln + 2lnx = -2lnx Add '2lnx' to each side of the equation. -18ln + 2lnx + 2lnx = -2lnx + 2lnx Combine like terms: 2lnx + 2lnx = 4lnx -18ln + 4lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -18ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-9 + 2x) = 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 '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 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 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Add '-2x' to each side of the equation. 2x + -2x = 9 + -2x Combine like terms: 2x + -2x = 0 0 = 9 + -2x Simplifying 0 = 9 + -2x 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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