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Simplifying U(x) = ln(0.5x) Multiply U * x xU = ln(0.5x) Remove parenthesis around (0.5x) xU = ln * 0.5x Reorder the terms for easier multiplication: xU = 0.5ln * x Multiply ln * x xU = 0.5lnx Solving xU = 0.5lnx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5lnx' to each side of the equation. -0.5lnx + xU = 0.5lnx + -0.5lnx Combine like terms: 0.5lnx + -0.5lnx = 0.0 -0.5lnx + xU = 0.0 Factor out the Greatest Common Factor (GCF), 'x'. x(-0.5ln + U) = 0.0Subproblem 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 '(-0.5ln + U)' equal to zero and attempt to solve: Simplifying -0.5ln + U = 0 Reorder the terms: U + -0.5ln = 0 Solving U + -0.5ln = 0 Move all terms containing x to the left, all other terms to the right. Add '-1U' to each side of the equation. U + -1U + -0.5ln = 0 + -1U Combine like terms: U + -1U = 0 0 + -0.5ln = 0 + -1U -0.5ln = 0 + -1U Remove the zero: -0.5ln = -1U Add '0.5ln' to each side of the equation. -0.5ln + 0.5ln = -1U + 0.5ln Combine like terms: -0.5ln + 0.5ln = 0.0 0.0 = -1U + 0.5ln Simplifying 0.0 = -1U + 0.5ln 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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