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Simplifying -2ln(X) + 6ln(X) = ln(27) + ln(X) Multiply ln * X -2lnX + 6ln(X) = ln(27) + ln(X) Multiply ln * X -2lnX + 6lnX = ln(27) + ln(X) Combine like terms: -2lnX + 6lnX = 4lnX 4lnX = ln(27) + ln(X) Reorder the terms for easier multiplication: 4lnX = 27ln + ln(X) Multiply ln * X 4lnX = 27ln + lnX Solving 4lnX = 27ln + lnX Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-27ln' to each side of the equation. -27ln + 4lnX = 27ln + -27ln + lnX Combine like terms: 27ln + -27ln = 0 -27ln + 4lnX = 0 + lnX -27ln + 4lnX = lnX Add '-1lnX' to each side of the equation. -27ln + 4lnX + -1lnX = lnX + -1lnX Combine like terms: 4lnX + -1lnX = 3lnX -27ln + 3lnX = lnX + -1lnX Combine like terms: lnX + -1lnX = 0 -27ln + 3lnX = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-9 + X) = 0 Ignore the factor 3.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 '(-9 + X)' equal to zero and attempt to solve: Simplifying -9 + X = 0 Solving -9 + X = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + X = 0 + 9 Combine like terms: -9 + 9 = 0 0 + X = 0 + 9 X = 0 + 9 Combine like terms: 0 + 9 = 9 X = 9 Add '-1X' to each side of the equation. X + -1X = 9 + -1X Combine like terms: X + -1X = 0 0 = 9 + -1X Simplifying 0 = 9 + -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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