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Simplifying 2ln(x + -1) = ln(9x) Reorder the terms: 2ln(-1 + x) = ln(9x) (-1 * 2ln + x * 2ln) = ln(9x) (-2ln + 2lnx) = ln(9x) Remove parenthesis around (9x) -2ln + 2lnx = ln * 9x Reorder the terms for easier multiplication: -2ln + 2lnx = 9ln * x Multiply ln * x -2ln + 2lnx = 9lnx Solving -2ln + 2lnx = 9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9lnx' to each side of the equation. -2ln + 2lnx + -9lnx = 9lnx + -9lnx Combine like terms: 2lnx + -9lnx = -7lnx -2ln + -7lnx = 9lnx + -9lnx Combine like terms: 9lnx + -9lnx = 0 -2ln + -7lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(2 + 7x) = 0 Ignore the factor -1.Subproblem 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 '(2 + 7x)' equal to zero and attempt to solve: Simplifying 2 + 7x = 0 Solving 2 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7x = 0 + -2 7x = 0 + -2 Combine like terms: 0 + -2 = -2 7x = -2 Add '-7x' to each side of the equation. 7x + -7x = -2 + -7x Combine like terms: 7x + -7x = 0 0 = -2 + -7x Simplifying 0 = -2 + -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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