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Simplifying ln(7x + -2) + ln(x + -1) = lnx Reorder the terms: ln(-2 + 7x) + ln(x + -1) = lnx (-2 * ln + 7x * ln) + ln(x + -1) = lnx (-2ln + 7lnx) + ln(x + -1) = lnx Reorder the terms: -2ln + 7lnx + ln(-1 + x) = lnx -2ln + 7lnx + (-1 * ln + x * ln) = lnx -2ln + 7lnx + (-1ln + lnx) = lnx Reorder the terms: -2ln + -1ln + 7lnx + lnx = lnx Combine like terms: -2ln + -1ln = -3ln -3ln + 7lnx + lnx = lnx Combine like terms: 7lnx + lnx = 8lnx -3ln + 8lnx = lnx Solving -3ln + 8lnx = 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. -3ln + 8lnx + -1lnx = lnx + -1lnx Combine like terms: 8lnx + -1lnx = 7lnx -3ln + 7lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -3ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 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 '(-3 + 7x)' equal to zero and attempt to solve: Simplifying -3 + 7x = 0 Solving -3 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 7x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 7x = 0 + 3 7x = 0 + 3 Combine like terms: 0 + 3 = 3 7x = 3 Add '-7x' to each side of the equation. 7x + -7x = 3 + -7x Combine like terms: 7x + -7x = 0 0 = 3 + -7x Simplifying 0 = 3 + -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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