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Simplifying ln(X + -1) = ln(7x) Reorder the terms: ln(-1 + X) = ln(7x) (-1 * ln + X * ln) = ln(7x) (-1ln + lnX) = ln(7x) Remove parenthesis around (7x) -1ln + lnX = ln * 7x Reorder the terms for easier multiplication: -1ln + lnX = 7ln * x Multiply ln * x -1ln + lnX = 7lnx Solving -1ln + lnX = 7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7lnx' to each side of the equation. -1ln + lnX + -7lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 -1ln + lnX + -7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1 + X + -7x) = 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 + -7x)' equal to zero and attempt to solve: Simplifying -1 + X + -7x = 0 Solving -1 + X + -7x = 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 + -7x = 0 + 1 Reorder the terms: -1 + 1 + X + -7x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + X + -7x = 0 + 1 X + -7x = 0 + 1 Combine like terms: 0 + 1 = 1 X + -7x = 1 Add '-1X' to each side of the equation. X + -1X + -7x = 1 + -1X Combine like terms: X + -1X = 0 0 + -7x = 1 + -1X -7x = 1 + -1X Add '7x' to each side of the equation. -7x + 7x = 1 + -1X + 7x Combine like terms: -7x + 7x = 0 0 = 1 + -1X + 7x Simplifying 0 = 1 + -1X + 7x 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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