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Simplifying x = ln(-5x) Remove parenthesis around (-5x) x = ln * -5x Reorder the terms for easier multiplication: x = -5ln * x Multiply ln * x x = -5lnx Solving x = -5lnx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5lnx' to each side of the equation. 5lnx + x = -5lnx + 5lnx Combine like terms: -5lnx + 5lnx = 0 5lnx + x = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(5ln + 1) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5ln + 1)' equal to zero and attempt to solve: Simplifying 5ln + 1 = 0 Reorder the terms: 1 + 5ln = 0 Solving 1 + 5ln = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5ln = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5ln = 0 + -1 5ln = 0 + -1 Combine like terms: 0 + -1 = -1 5ln = -1 Add '-5ln' to each side of the equation. 5ln + -5ln = -1 + -5ln Combine like terms: 5ln + -5ln = 0 0 = -1 + -5ln Simplifying 0 = -1 + -5ln The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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