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Simplifying 2ln(x) = ln(4) + ln(5 + -2x) Multiply ln * x 2lnx = ln(4) + ln(5 + -2x) Reorder the terms for easier multiplication: 2lnx = 4ln + ln(5 + -2x) 2lnx = 4ln + (5 * ln + -2x * ln) 2lnx = 4ln + (5ln + -2lnx) Combine like terms: 4ln + 5ln = 9ln 2lnx = 9ln + -2lnx Solving 2lnx = 9ln + -2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. -9ln + 2lnx = 9ln + -9ln + -2lnx Combine like terms: 9ln + -9ln = 0 -9ln + 2lnx = 0 + -2lnx -9ln + 2lnx = -2lnx Add '2lnx' to each side of the equation. -9ln + 2lnx + 2lnx = -2lnx + 2lnx Combine like terms: 2lnx + 2lnx = 4lnx -9ln + 4lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -9ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + 4x) = 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 '(-9 + 4x)' equal to zero and attempt to solve: Simplifying -9 + 4x = 0 Solving -9 + 4x = 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 + 4x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4x = 0 + 9 4x = 0 + 9 Combine like terms: 0 + 9 = 9 4x = 9 Add '-4x' to each side of the equation. 4x + -4x = 9 + -4x Combine like terms: 4x + -4x = 0 0 = 9 + -4x Simplifying 0 = 9 + -4x 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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