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Simplifying 4ln(2) + ln(x + -3) = ln(96) Reorder the terms for easier multiplication: 4 * 2ln + ln(x + -3) = ln(96) Multiply 4 * 2 8ln + ln(x + -3) = ln(96) Reorder the terms: 8ln + ln(-3 + x) = ln(96) 8ln + (-3 * ln + x * ln) = ln(96) 8ln + (-3ln + lnx) = ln(96) Combine like terms: 8ln + -3ln = 5ln 5ln + lnx = ln(96) Reorder the terms for easier multiplication: 5ln + lnx = 96ln Solving 5ln + 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. 5ln + -96ln + lnx = 96ln + -96ln Combine like terms: 5ln + -96ln = -91ln -91ln + lnx = 96ln + -96ln Combine like terms: 96ln + -96ln = 0 -91ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-91 + 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 '(-91 + x)' equal to zero and attempt to solve: Simplifying -91 + x = 0 Solving -91 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '91' to each side of the equation. -91 + 91 + x = 0 + 91 Combine like terms: -91 + 91 = 0 0 + x = 0 + 91 x = 0 + 91 Combine like terms: 0 + 91 = 91 x = 91 Add '-1x' to each side of the equation. x + -1x = 91 + -1x Combine like terms: x + -1x = 0 0 = 91 + -1x Simplifying 0 = 91 + -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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