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