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Simplifying 0 = ln(8x + 2) Reorder the terms: 0 = ln(2 + 8x) 0 = (2 * ln + 8x * ln) 0 = (2ln + 8lnx) Solving 0 = 2ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. 0 + -2ln = 2ln + -2ln + 8lnx Remove the zero: -2ln = 2ln + -2ln + 8lnx Combine like terms: 2ln + -2ln = 0 -2ln = 0 + 8lnx -2ln = 8lnx Add '-8lnx' to each side of the equation. -2ln + -8lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 -2ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(1 + 4x) = 0 Ignore the factor -2.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 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Add '-4x' to each side of the equation. 4x + -4x = -1 + -4x Combine like terms: 4x + -4x = 0 0 = -1 + -4x Simplifying 0 = -1 + -4x 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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