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Simplifying ln(4x + 4) + -1ln(3x + -1) = ln(x + 1) Reorder the terms: ln(4 + 4x) + -1ln(3x + -1) = ln(x + 1) (4 * ln + 4x * ln) + -1ln(3x + -1) = ln(x + 1) (4ln + 4lnx) + -1ln(3x + -1) = ln(x + 1) Reorder the terms: 4ln + 4lnx + -1ln(-1 + 3x) = ln(x + 1) 4ln + 4lnx + (-1 * -1ln + 3x * -1ln) = ln(x + 1) 4ln + 4lnx + (1ln + -3lnx) = ln(x + 1) Reorder the terms: 4ln + 1ln + 4lnx + -3lnx = ln(x + 1) Combine like terms: 4ln + 1ln = 5ln 5ln + 4lnx + -3lnx = ln(x + 1) Combine like terms: 4lnx + -3lnx = 1lnx 5ln + 1lnx = ln(x + 1) Reorder the terms: 5ln + 1lnx = ln(1 + x) 5ln + 1lnx = (1 * ln + x * ln) 5ln + 1lnx = (1ln + lnx) Solving 5ln + 1lnx = 1ln + lnx 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. 5ln + -1ln + 1lnx = 1ln + -1ln + lnx Combine like terms: 5ln + -1ln = 4ln 4ln + 1lnx = 1ln + -1ln + lnx Combine like terms: 1ln + -1ln = 0 4ln + 1lnx = 0 + lnx 4ln + 1lnx = lnx Add '-1lnx' to each side of the equation. 4ln + 1lnx + -1lnx = lnx + -1lnx Combine like terms: 1lnx + -1lnx = 0 4ln + 0 = lnx + -1lnx 4ln = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 4ln = 0 Divide each side by '4'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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