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