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Simplifying ln(8 + -6x) + -2ln(x) = ln(2) (8 * ln + -6x * ln) + -2ln(x) = ln(2) (8ln + -6lnx) + -2ln(x) = ln(2) Multiply ln * x 8ln + -6lnx + -2lnx = ln(2) Combine like terms: -6lnx + -2lnx = -8lnx 8ln + -8lnx = ln(2) Reorder the terms for easier multiplication: 8ln + -8lnx = 2ln Solving 8ln + -8lnx = 2ln 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. 8ln + -2ln + -8lnx = 2ln + -2ln Combine like terms: 8ln + -2ln = 6ln 6ln + -8lnx = 2ln + -2ln Combine like terms: 2ln + -2ln = 0 6ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(3 + -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 '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Add '4x' to each side of the equation. -4x + 4x = -3 + 4x Combine like terms: -4x + 4x = 0 0 = -3 + 4x Simplifying 0 = -3 + 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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