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Simplifying 2lnx + -1ln(2x + -7) = ln(9x) + -1ln(x + 2) Reorder the terms: 2lnx + -1ln(-7 + 2x) = ln(9x) + -1ln(x + 2) 2lnx + (-7 * -1ln + 2x * -1ln) = ln(9x) + -1ln(x + 2) 2lnx + (7ln + -2lnx) = ln(9x) + -1ln(x + 2) Reorder the terms: 7ln + 2lnx + -2lnx = ln(9x) + -1ln(x + 2) Combine like terms: 2lnx + -2lnx = 0 7ln + 0 = ln(9x) + -1ln(x + 2) 7ln = ln(9x) + -1ln(x + 2) Remove parenthesis around (9x) 7ln = ln * 9x + -1ln(x + 2) Reorder the terms for easier multiplication: 7ln = 9ln * x + -1ln(x + 2) Multiply ln * x 7ln = 9lnx + -1ln(x + 2) Reorder the terms: 7ln = 9lnx + -1ln(2 + x) 7ln = 9lnx + (2 * -1ln + x * -1ln) 7ln = 9lnx + (-2ln + -1lnx) Reorder the terms: 7ln = -2ln + 9lnx + -1lnx Combine like terms: 9lnx + -1lnx = 8lnx 7ln = -2ln + 8lnx Solving 7ln = -2ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 7ln + 2ln = -2ln + 2ln + 8lnx Combine like terms: 7ln + 2ln = 9ln 9ln = -2ln + 2ln + 8lnx Combine like terms: -2ln + 2ln = 0 9ln = 0 + 8lnx 9ln = 8lnx Add '-8lnx' to each side of the equation. 9ln + -8lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 9ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + -8x) = 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 '(9 + -8x)' equal to zero and attempt to solve: Simplifying 9 + -8x = 0 Solving 9 + -8x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -8x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8x = 0 + -9 -8x = 0 + -9 Combine like terms: 0 + -9 = -9 -8x = -9 Add '8x' to each side of the equation. -8x + 8x = -9 + 8x Combine like terms: -8x + 8x = 0 0 = -9 + 8x Simplifying 0 = -9 + 8x 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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