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Simplifying ln(4x + -5) + -1ln(2x + -5) = ln(2x + 1) Reorder the terms: ln(-5 + 4x) + -1ln(2x + -5) = ln(2x + 1) (-5 * ln + 4x * ln) + -1ln(2x + -5) = ln(2x + 1) (-5ln + 4lnx) + -1ln(2x + -5) = ln(2x + 1) Reorder the terms: -5ln + 4lnx + -1ln(-5 + 2x) = ln(2x + 1) -5ln + 4lnx + (-5 * -1ln + 2x * -1ln) = ln(2x + 1) -5ln + 4lnx + (5ln + -2lnx) = ln(2x + 1) Reorder the terms: -5ln + 5ln + 4lnx + -2lnx = ln(2x + 1) Combine like terms: -5ln + 5ln = 0 0 + 4lnx + -2lnx = ln(2x + 1) 4lnx + -2lnx = ln(2x + 1) Combine like terms: 4lnx + -2lnx = 2lnx 2lnx = ln(2x + 1) Reorder the terms: 2lnx = ln(1 + 2x) 2lnx = (1 * ln + 2x * ln) 2lnx = (1ln + 2lnx) Add '-2lnx' to each side of the equation. 2lnx + -2lnx = 1ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 0 = 1ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 0 = 1ln + 0 0 = 1ln Solving 0 = 1ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 0 + -1ln = 1ln + -1ln Remove the zero: -1ln = 1ln + -1ln Combine like terms: 1ln + -1ln = 0 -1ln = 0 Divide each side by '-1'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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