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