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Simplifying ln(x + -1) + ln(4) = ln(2x + 4) + -1ln(2) Reorder the terms: ln(-1 + x) + ln(4) = ln(2x + 4) + -1ln(2) (-1 * ln + x * ln) + ln(4) = ln(2x + 4) + -1ln(2) (-1ln + lnx) + ln(4) = ln(2x + 4) + -1ln(2) Reorder the terms for easier multiplication: -1ln + lnx + 4ln = ln(2x + 4) + -1ln(2) Reorder the terms: -1ln + 4ln + lnx = ln(2x + 4) + -1ln(2) Combine like terms: -1ln + 4ln = 3ln 3ln + lnx = ln(2x + 4) + -1ln(2) Reorder the terms: 3ln + lnx = ln(4 + 2x) + -1ln(2) 3ln + lnx = (4 * ln + 2x * ln) + -1ln(2) 3ln + lnx = (4ln + 2lnx) + -1ln(2) Reorder the terms for easier multiplication: 3ln + lnx = 4ln + 2lnx + -1 * 2ln Multiply -1 * 2 3ln + lnx = 4ln + 2lnx + -2ln Reorder the terms: 3ln + lnx = 4ln + -2ln + 2lnx Combine like terms: 4ln + -2ln = 2ln 3ln + lnx = 2ln + 2lnx Solving 3ln + lnx = 2ln + 2lnx 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. 3ln + -2ln + lnx = 2ln + -2ln + 2lnx Combine like terms: 3ln + -2ln = 1ln 1ln + lnx = 2ln + -2ln + 2lnx Combine like terms: 2ln + -2ln = 0 1ln + lnx = 0 + 2lnx 1ln + lnx = 2lnx Add '-2lnx' to each side of the equation. 1ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx 1ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 1ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -1x) = 0Subproblem 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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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