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