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Simplifying 4ln(2) + ln(x + -2) = ln(96) Reorder the terms for easier multiplication: 4 * 2ln + ln(x + -2) = ln(96) Multiply 4 * 2 8ln + ln(x + -2) = ln(96) Reorder the terms: 8ln + ln(-2 + x) = ln(96) 8ln + (-2 * ln + x * ln) = ln(96) 8ln + (-2ln + lnx) = ln(96) Combine like terms: 8ln + -2ln = 6ln 6ln + lnx = ln(96) Reorder the terms for easier multiplication: 6ln + lnx = 96ln Solving 6ln + lnx = 96ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-96ln' to each side of the equation. 6ln + -96ln + lnx = 96ln + -96ln Combine like terms: 6ln + -96ln = -90ln -90ln + lnx = 96ln + -96ln Combine like terms: 96ln + -96ln = 0 -90ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-90 + 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 '(-90 + x)' equal to zero and attempt to solve: Simplifying -90 + x = 0 Solving -90 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 0 + 90 Combine like terms: -90 + 90 = 0 0 + x = 0 + 90 x = 0 + 90 Combine like terms: 0 + 90 = 90 x = 90 Add '-1x' to each side of the equation. x + -1x = 90 + -1x Combine like terms: x + -1x = 0 0 = 90 + -1x Simplifying 0 = 90 + -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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