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Simplifying ln(2x + 1) + ln(x + -7) = lnx + ln(2x + -3) Reorder the terms: ln(1 + 2x) + ln(x + -7) = lnx + ln(2x + -3) (1 * ln + 2x * ln) + ln(x + -7) = lnx + ln(2x + -3) (1ln + 2lnx) + ln(x + -7) = lnx + ln(2x + -3) Reorder the terms: 1ln + 2lnx + ln(-7 + x) = lnx + ln(2x + -3) 1ln + 2lnx + (-7 * ln + x * ln) = lnx + ln(2x + -3) 1ln + 2lnx + (-7ln + lnx) = lnx + ln(2x + -3) Reorder the terms: 1ln + -7ln + 2lnx + lnx = lnx + ln(2x + -3) Combine like terms: 1ln + -7ln = -6ln -6ln + 2lnx + lnx = lnx + ln(2x + -3) Combine like terms: 2lnx + lnx = 3lnx -6ln + 3lnx = lnx + ln(2x + -3) Reorder the terms: -6ln + 3lnx = lnx + ln(-3 + 2x) -6ln + 3lnx = lnx + (-3 * ln + 2x * ln) -6ln + 3lnx = lnx + (-3ln + 2lnx) Reorder the terms: -6ln + 3lnx = -3ln + lnx + 2lnx Combine like terms: lnx + 2lnx = 3lnx -6ln + 3lnx = -3ln + 3lnx Add '-3lnx' to each side of the equation. -6ln + 3lnx + -3lnx = -3ln + 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -6ln + 0 = -3ln + 3lnx + -3lnx -6ln = -3ln + 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -6ln = -3ln + 0 -6ln = -3ln Solving -6ln = -3ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3ln' to each side of the equation. -6ln + 3ln = -3ln + 3ln Combine like terms: -6ln + 3ln = -3ln -3ln = -3ln + 3ln Combine like terms: -3ln + 3ln = 0 -3ln = 0 Divide each side by '-3'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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