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Simplifying ln(X + 7) + -1ln(x + 8) = lnx Reorder the terms: ln(7 + X) + -1ln(x + 8) = lnx (7 * ln + X * ln) + -1ln(x + 8) = lnx (7ln + lnX) + -1ln(x + 8) = lnx Reorder the terms: 7ln + lnX + -1ln(8 + x) = lnx 7ln + lnX + (8 * -1ln + x * -1ln) = lnx 7ln + lnX + (-8ln + -1lnx) = lnx Reorder the terms: 7ln + -8ln + lnX + -1lnx = lnx Combine like terms: 7ln + -8ln = -1ln -1ln + lnX + -1lnx = lnx Solving -1ln + lnX + -1lnx = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. -1ln + lnX + -1lnx + -1lnx = lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx -1ln + lnX + -2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -1ln + lnX + -2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1 + X + -2x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1 + X + -2x)' equal to zero and attempt to solve: Simplifying -1 + X + -2x = 0 Solving -1 + X + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + X + 1 + -2x = 0 + 1 Reorder the terms: -1 + 1 + X + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + X + -2x = 0 + 1 X + -2x = 0 + 1 Combine like terms: 0 + 1 = 1 X + -2x = 1 Add '-1X' to each side of the equation. X + -1X + -2x = 1 + -1X Combine like terms: X + -1X = 0 0 + -2x = 1 + -1X -2x = 1 + -1X Add '2x' to each side of the equation. -2x + 2x = 1 + -1X + 2x Combine like terms: -2x + 2x = 0 0 = 1 + -1X + 2x Simplifying 0 = 1 + -1X + 2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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