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Simplifying ln(2x + -1) = ln(3x + 9) Reorder the terms: ln(-1 + 2x) = ln(3x + 9) (-1 * ln + 2x * ln) = ln(3x + 9) (-1ln + 2lnx) = ln(3x + 9) Reorder the terms: -1ln + 2lnx = ln(9 + 3x) -1ln + 2lnx = (9 * ln + 3x * ln) -1ln + 2lnx = (9ln + 3lnx) Solving -1ln + 2lnx = 9ln + 3lnx 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. -1ln + -9ln + 2lnx = 9ln + -9ln + 3lnx Combine like terms: -1ln + -9ln = -10ln -10ln + 2lnx = 9ln + -9ln + 3lnx Combine like terms: 9ln + -9ln = 0 -10ln + 2lnx = 0 + 3lnx -10ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. -10ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx -10ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -10ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -1x 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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