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Simplifying ln(x + 1) + -1ln(3x) = 1 + -1ln(2) Reorder the terms: ln(1 + x) + -1ln(3x) = 1 + -1ln(2) (1 * ln + x * ln) + -1ln(3x) = 1 + -1ln(2) (1ln + lnx) + -1ln(3x) = 1 + -1ln(2) Remove parenthesis around (3x) 1ln + lnx + -1ln * 3x = 1 + -1ln(2) Reorder the terms for easier multiplication: 1ln + lnx + -1 * 3ln * x = 1 + -1ln(2) Multiply -1 * 3 1ln + lnx + -3ln * x = 1 + -1ln(2) Multiply ln * x 1ln + lnx + -3lnx = 1 + -1ln(2) Combine like terms: lnx + -3lnx = -2lnx 1ln + -2lnx = 1 + -1ln(2) Reorder the terms for easier multiplication: 1ln + -2lnx = 1 + -1 * 2ln Multiply -1 * 2 1ln + -2lnx = 1 + -2ln Solving 1ln + -2lnx = 1 + -2ln 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. 1ln + 2ln + -2lnx = 1 + -2ln + 2ln Combine like terms: 1ln + 2ln = 3ln 3ln + -2lnx = 1 + -2ln + 2ln Combine like terms: -2ln + 2ln = 0 3ln + -2lnx = 1 + 0 3ln + -2lnx = 1 Reorder the terms: -1 + 3ln + -2lnx = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 3ln + -2lnx = 0 The solution to this equation could not be determined.
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