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Simplifying ln(2x + -1) + -1ln(3) = ln(9) Reorder the terms: ln(-1 + 2x) + -1ln(3) = ln(9) (-1 * ln + 2x * ln) + -1ln(3) = ln(9) (-1ln + 2lnx) + -1ln(3) = ln(9) Reorder the terms for easier multiplication: -1ln + 2lnx + -1 * 3ln = ln(9) Multiply -1 * 3 -1ln + 2lnx + -3ln = ln(9) Reorder the terms: -1ln + -3ln + 2lnx = ln(9) Combine like terms: -1ln + -3ln = -4ln -4ln + 2lnx = ln(9) Reorder the terms for easier multiplication: -4ln + 2lnx = 9ln Solving -4ln + 2lnx = 9ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. -4ln + -9ln + 2lnx = 9ln + -9ln Combine like terms: -4ln + -9ln = -13ln -13ln + 2lnx = 9ln + -9ln Combine like terms: 9ln + -9ln = 0 -13ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 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 '(-13 + 2x)' equal to zero and attempt to solve: Simplifying -13 + 2x = 0 Solving -13 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2x = 0 + 13 2x = 0 + 13 Combine like terms: 0 + 13 = 13 2x = 13 Add '-2x' to each side of the equation. 2x + -2x = 13 + -2x Combine like terms: 2x + -2x = 0 0 = 13 + -2x Simplifying 0 = 13 + -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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