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Simplifying ln(x + 3) + -4 = ln(x + -7) Reorder the terms: ln(3 + x) + -4 = ln(x + -7) (3 * ln + x * ln) + -4 = ln(x + -7) (3ln + lnx) + -4 = ln(x + -7) Reorder the terms: -4 + 3ln + lnx = ln(x + -7) Reorder the terms: -4 + 3ln + lnx = ln(-7 + x) -4 + 3ln + lnx = (-7 * ln + x * ln) -4 + 3ln + lnx = (-7ln + lnx) Add '-1lnx' to each side of the equation. -4 + 3ln + lnx + -1lnx = -7ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -4 + 3ln + 0 = -7ln + lnx + -1lnx -4 + 3ln = -7ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -4 + 3ln = -7ln + 0 -4 + 3ln = -7ln Solving -4 + 3ln = -7ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '7ln' to each side of the equation. -4 + 3ln + 7ln = -7ln + 7ln Combine like terms: 3ln + 7ln = 10ln -4 + 10ln = -7ln + 7ln Combine like terms: -7ln + 7ln = 0 -4 + 10ln = 0 Add '4' to each side of the equation. -4 + 4 + 10ln = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 10ln = 0 + 4 10ln = 0 + 4 Combine like terms: 0 + 4 = 4 10ln = 4 Divide each side by '10n'. l = 0.4n-1 Simplifying l = 0.4n-1
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