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