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