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