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