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Simplifying 2ln(x + -3) = ln(x + 5) + ln(x + 3) Reorder the terms: 2ln(-3 + x) = ln(x + 5) + ln(x + 3) (-3 * 2ln + x * 2ln) = ln(x + 5) + ln(x + 3) (-6ln + 2lnx) = ln(x + 5) + ln(x + 3) Reorder the terms: -6ln + 2lnx = ln(5 + x) + ln(x + 3) -6ln + 2lnx = (5 * ln + x * ln) + ln(x + 3) -6ln + 2lnx = (5ln + lnx) + ln(x + 3) Reorder the terms: -6ln + 2lnx = 5ln + lnx + ln(3 + x) -6ln + 2lnx = 5ln + lnx + (3 * ln + x * ln) -6ln + 2lnx = 5ln + lnx + (3ln + lnx) Reorder the terms: -6ln + 2lnx = 5ln + 3ln + lnx + lnx Combine like terms: 5ln + 3ln = 8ln -6ln + 2lnx = 8ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx -6ln + 2lnx = 8ln + 2lnx Add '-2lnx' to each side of the equation. -6ln + 2lnx + -2lnx = 8ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -6ln + 0 = 8ln + 2lnx + -2lnx -6ln = 8ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -6ln = 8ln + 0 -6ln = 8ln Solving -6ln = 8ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. -6ln + -8ln = 8ln + -8ln Combine like terms: -6ln + -8ln = -14ln -14ln = 8ln + -8ln Combine like terms: 8ln + -8ln = 0 -14ln = 0 Divide each side by '-14'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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