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Simplifying ln(4x + 7) = 13 + ln(x + -5) Reorder the terms: ln(7 + 4x) = 13 + ln(x + -5) (7 * ln + 4x * ln) = 13 + ln(x + -5) (7ln + 4lnx) = 13 + ln(x + -5) Reorder the terms: 7ln + 4lnx = 13 + ln(-5 + x) 7ln + 4lnx = 13 + (-5 * ln + x * ln) 7ln + 4lnx = 13 + (-5ln + lnx) Solving 7ln + 4lnx = 13 + -5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 7ln + 5ln + 4lnx = 13 + -5ln + 5ln + lnx Combine like terms: 7ln + 5ln = 12ln 12ln + 4lnx = 13 + -5ln + 5ln + lnx Combine like terms: -5ln + 5ln = 0 12ln + 4lnx = 13 + 0 + lnx 12ln + 4lnx = 13 + lnx Add '-1lnx' to each side of the equation. 12ln + 4lnx + -1lnx = 13 + lnx + -1lnx Combine like terms: 4lnx + -1lnx = 3lnx 12ln + 3lnx = 13 + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 12ln + 3lnx = 13 + 0 12ln + 3lnx = 13 Reorder the terms: -13 + 12ln + 3lnx = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 12ln + 3lnx = 0 The solution to this equation could not be determined.
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