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Simplifying ln(3x + 5) + -1ln(2x + 1) = 3 + -1ln(x) Reorder the terms: ln(5 + 3x) + -1ln(2x + 1) = 3 + -1ln(x) (5 * ln + 3x * ln) + -1ln(2x + 1) = 3 + -1ln(x) (5ln + 3lnx) + -1ln(2x + 1) = 3 + -1ln(x) Reorder the terms: 5ln + 3lnx + -1ln(1 + 2x) = 3 + -1ln(x) 5ln + 3lnx + (1 * -1ln + 2x * -1ln) = 3 + -1ln(x) 5ln + 3lnx + (-1ln + -2lnx) = 3 + -1ln(x) Reorder the terms: 5ln + -1ln + 3lnx + -2lnx = 3 + -1ln(x) Combine like terms: 5ln + -1ln = 4ln 4ln + 3lnx + -2lnx = 3 + -1ln(x) Combine like terms: 3lnx + -2lnx = 1lnx 4ln + 1lnx = 3 + -1ln(x) Multiply ln * x 4ln + 1lnx = 3 + -1lnx Solving 4ln + 1lnx = 3 + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'lnx' to each side of the equation. 4ln + 1lnx + lnx = 3 + -1lnx + lnx Combine like terms: 1lnx + lnx = 2lnx 4ln + 2lnx = 3 + -1lnx + lnx Combine like terms: -1lnx + lnx = 0 4ln + 2lnx = 3 + 0 4ln + 2lnx = 3 Reorder the terms: -3 + 4ln + 2lnx = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 4ln + 2lnx = 0 The solution to this equation could not be determined.
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