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Simplifying 2lnx + ln(x + -4) = ln * 5 + ln * x Reorder the terms: 2lnx + ln(-4 + x) = ln * 5 + ln * x 2lnx + (-4 * ln + x * ln) = ln * 5 + ln * x 2lnx + (-4ln + lnx) = ln * 5 + ln * x Reorder the terms: -4ln + 2lnx + lnx = ln * 5 + ln * x Combine like terms: 2lnx + lnx = 3lnx -4ln + 3lnx = ln * 5 + ln * x Reorder the terms for easier multiplication: -4ln + 3lnx = 5ln + ln * x Multiply ln * x -4ln + 3lnx = 5ln + lnx Solving -4ln + 3lnx = 5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -4ln + -5ln + 3lnx = 5ln + -5ln + lnx Combine like terms: -4ln + -5ln = -9ln -9ln + 3lnx = 5ln + -5ln + lnx Combine like terms: 5ln + -5ln = 0 -9ln + 3lnx = 0 + lnx -9ln + 3lnx = lnx Add '-1lnx' to each side of the equation. -9ln + 3lnx + -1lnx = lnx + -1lnx Combine like terms: 3lnx + -1lnx = 2lnx -9ln + 2lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -9ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + 2x) = 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 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 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 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Add '-2x' to each side of the equation. 2x + -2x = 9 + -2x Combine like terms: 2x + -2x = 0 0 = 9 + -2x Simplifying 0 = 9 + -2x 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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