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Simplifying ln(x) + 2ln(4) = 3ln(6) + -1ln(2) Multiply ln * x lnx + 2ln(4) = 3ln(6) + -1ln(2) Reorder the terms for easier multiplication: lnx + 2 * 4ln = 3ln(6) + -1ln(2) Multiply 2 * 4 lnx + 8ln = 3ln(6) + -1ln(2) Reorder the terms: 8ln + lnx = 3ln(6) + -1ln(2) Reorder the terms for easier multiplication: 8ln + lnx = 3 * 6ln + -1ln(2) Multiply 3 * 6 8ln + lnx = 18ln + -1ln(2) Reorder the terms for easier multiplication: 8ln + lnx = 18ln + -1 * 2ln Multiply -1 * 2 8ln + lnx = 18ln + -2ln Combine like terms: 18ln + -2ln = 16ln 8ln + lnx = 16ln Solving 8ln + lnx = 16ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-16ln' to each side of the equation. 8ln + -16ln + lnx = 16ln + -16ln Combine like terms: 8ln + -16ln = -8ln -8ln + lnx = 16ln + -16ln Combine like terms: 16ln + -16ln = 0 -8ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -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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