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Simplifying 2ln(3x + 1) = ln(6x + 10) Reorder the terms: 2ln(1 + 3x) = ln(6x + 10) (1 * 2ln + 3x * 2ln) = ln(6x + 10) (2ln + 6lnx) = ln(6x + 10) Reorder the terms: 2ln + 6lnx = ln(10 + 6x) 2ln + 6lnx = (10 * ln + 6x * ln) 2ln + 6lnx = (10ln + 6lnx) Add '-6lnx' to each side of the equation. 2ln + 6lnx + -6lnx = 10ln + 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 2ln + 0 = 10ln + 6lnx + -6lnx 2ln = 10ln + 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 2ln = 10ln + 0 2ln = 10ln Solving 2ln = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 2ln + -10ln = 10ln + -10ln Combine like terms: 2ln + -10ln = -8ln -8ln = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -8ln = 0 Divide each side by '-8'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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