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Simplifying 2ln(x) = ln(6x + -8) Multiply ln * x 2lnx = ln(6x + -8) Reorder the terms: 2lnx = ln(-8 + 6x) 2lnx = (-8 * ln + 6x * ln) 2lnx = (-8ln + 6lnx) Solving 2lnx = -8ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8ln' to each side of the equation. 8ln + 2lnx = -8ln + 8ln + 6lnx Combine like terms: -8ln + 8ln = 0 8ln + 2lnx = 0 + 6lnx 8ln + 2lnx = 6lnx Add '-6lnx' to each side of the equation. 8ln + 2lnx + -6lnx = 6lnx + -6lnx Combine like terms: 2lnx + -6lnx = -4lnx 8ln + -4lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 8ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(2 + -1x) = 0 Ignore the factor 4.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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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