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Simplifying ln(x + 1) + ln(x + -1) = ln(3) + 5ln(3) Reorder the terms: ln(1 + x) + ln(x + -1) = ln(3) + 5ln(3) (1 * ln + x * ln) + ln(x + -1) = ln(3) + 5ln(3) (1ln + lnx) + ln(x + -1) = ln(3) + 5ln(3) Reorder the terms: 1ln + lnx + ln(-1 + x) = ln(3) + 5ln(3) 1ln + lnx + (-1 * ln + x * ln) = ln(3) + 5ln(3) 1ln + lnx + (-1ln + lnx) = ln(3) + 5ln(3) Reorder the terms: 1ln + -1ln + lnx + lnx = ln(3) + 5ln(3) Combine like terms: 1ln + -1ln = 0 0 + lnx + lnx = ln(3) + 5ln(3) lnx + lnx = ln(3) + 5ln(3) Combine like terms: lnx + lnx = 2lnx 2lnx = ln(3) + 5ln(3) Reorder the terms for easier multiplication: 2lnx = 3ln + 5ln(3) Reorder the terms for easier multiplication: 2lnx = 3ln + 5 * 3ln Multiply 5 * 3 2lnx = 3ln + 15ln Combine like terms: 3ln + 15ln = 18ln 2lnx = 18ln Solving 2lnx = 18ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. -18ln + 2lnx = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 -18ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-9 + 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 '(-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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