3ln(x)+ln(y)=ln(2)

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Solution for 3ln(x)+ln(y)=ln(2) equation:


Simplifying
3ln(x) + ln(y) = ln(2)

Multiply ln * x
3lnx + ln(y) = ln(2)

Multiply ln * y
3lnx + lny = ln(2)

Reorder the terms for easier multiplication:
3lnx + lny = 2ln

Solving
3lnx + lny = 2ln

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-2ln' to each side of the equation.
3lnx + -2ln + lny = 2ln + -2ln

Reorder the terms:
-2ln + 3lnx + lny = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
-2ln + 3lnx + lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 3x + y) = 0

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 + 3x + y)' equal to zero and attempt to solve: Simplifying -2 + 3x + y = 0 Solving -2 + 3x + 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 + 3x + 2 + y = 0 + 2 Reorder the terms: -2 + 2 + 3x + y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x + y = 0 + 2 3x + y = 0 + 2 Combine like terms: 0 + 2 = 2 3x + y = 2 Add '-3x' to each side of the equation. 3x + -3x + y = 2 + -3x Combine like terms: 3x + -3x = 0 0 + y = 2 + -3x y = 2 + -3x Add '-1y' to each side of the equation. y + -1y = 2 + -3x + -1y Combine like terms: y + -1y = 0 0 = 2 + -3x + -1y Simplifying 0 = 2 + -3x + -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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