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Simplifying 2ln(x) = 2ln(2) + ln(x + 8) Multiply ln * x 2lnx = 2ln(2) + ln(x + 8) Reorder the terms for easier multiplication: 2lnx = 2 * 2ln + ln(x + 8) Multiply 2 * 2 2lnx = 4ln + ln(x + 8) Reorder the terms: 2lnx = 4ln + ln(8 + x) 2lnx = 4ln + (8 * ln + x * ln) 2lnx = 4ln + (8ln + lnx) Combine like terms: 4ln + 8ln = 12ln 2lnx = 12ln + lnx Solving 2lnx = 12ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. -12ln + 2lnx = 12ln + -12ln + lnx Combine like terms: 12ln + -12ln = 0 -12ln + 2lnx = 0 + lnx -12ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -12ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -12ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -12ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-12 + x) = 0Subproblem 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 '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Add '-1x' to each side of the equation. x + -1x = 12 + -1x Combine like terms: x + -1x = 0 0 = 12 + -1x Simplifying 0 = 12 + -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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