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