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Simplifying ln(x + 2) + ln(2x + 1) = 0 Reorder the terms: ln(2 + x) + ln(2x + 1) = 0 (2 * ln + x * ln) + ln(2x + 1) = 0 (2ln + lnx) + ln(2x + 1) = 0 Reorder the terms: 2ln + lnx + ln(1 + 2x) = 0 2ln + lnx + (1 * ln + 2x * ln) = 0 2ln + lnx + (1ln + 2lnx) = 0 Reorder the terms: 2ln + 1ln + lnx + 2lnx = 0 Combine like terms: 2ln + 1ln = 3ln 3ln + lnx + 2lnx = 0 Combine like terms: lnx + 2lnx = 3lnx 3ln + 3lnx = 0 Solving 3ln + 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), '3ln'. 3ln(1 + x) = 0 Ignore the factor 3.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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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