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Simplifying ln(x + -4) + ln(x + -16) = 6ln(2) Reorder the terms: ln(-4 + x) + ln(x + -16) = 6ln(2) (-4 * ln + x * ln) + ln(x + -16) = 6ln(2) (-4ln + lnx) + ln(x + -16) = 6ln(2) Reorder the terms: -4ln + lnx + ln(-16 + x) = 6ln(2) -4ln + lnx + (-16 * ln + x * ln) = 6ln(2) -4ln + lnx + (-16ln + lnx) = 6ln(2) Reorder the terms: -4ln + -16ln + lnx + lnx = 6ln(2) Combine like terms: -4ln + -16ln = -20ln -20ln + lnx + lnx = 6ln(2) Combine like terms: lnx + lnx = 2lnx -20ln + 2lnx = 6ln(2) Reorder the terms for easier multiplication: -20ln + 2lnx = 6 * 2ln Multiply 6 * 2 -20ln + 2lnx = 12ln Solving -20ln + 2lnx = 12ln 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. -20ln + -12ln + 2lnx = 12ln + -12ln Combine like terms: -20ln + -12ln = -32ln -32ln + 2lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -32ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-16 + x) = 0 Ignore the factor 2.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 '(-16 + x)' equal to zero and attempt to solve: Simplifying -16 + x = 0 Solving -16 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x = 0 + 16 x = 0 + 16 Combine like terms: 0 + 16 = 16 x = 16 Add '-1x' to each side of the equation. x + -1x = 16 + -1x Combine like terms: x + -1x = 0 0 = 16 + -1x Simplifying 0 = 16 + -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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