Ln(2y-1)-ln(3-y)=1

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Solution for Ln(2y-1)-ln(3-y)=1 equation:


Simplifying
Ln(2y + -1) + -1ln(3 + -1y) = 1

Reorder the terms:
nL(-1 + 2y) + -1ln(3 + -1y) = 1
(-1 * nL + 2y * nL) + -1ln(3 + -1y) = 1
(-1nL + 2nyL) + -1ln(3 + -1y) = 1
-1nL + 2nyL + (3 * -1ln + -1y * -1ln) = 1
-1nL + 2nyL + (-3ln + 1lny) = 1

Reorder the terms:
-3ln + 1lny + -1nL + 2nyL = 1

Solving
-3ln + 1lny + -1nL + 2nyL = 1

Solving for variable 'l'.

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

Add 'nL' to each side of the equation.
-3ln + 1lny + -1nL + nL + 2nyL = 1 + nL

Combine like terms: -1nL + nL = 0
-3ln + 1lny + 0 + 2nyL = 1 + nL
-3ln + 1lny + 2nyL = 1 + nL

Add '-2nyL' to each side of the equation.
-3ln + 1lny + 2nyL + -2nyL = 1 + nL + -2nyL

Combine like terms: 2nyL + -2nyL = 0
-3ln + 1lny + 0 = 1 + nL + -2nyL
-3ln + 1lny = 1 + nL + -2nyL

Reorder the terms:
-1 + -3ln + 1lny + -1nL + 2nyL = 1 + nL + -2nyL + -1 + -1nL + 2nyL

Reorder the terms:
-1 + -3ln + 1lny + -1nL + 2nyL = 1 + -1 + nL + -1nL + -2nyL + 2nyL

Combine like terms: 1 + -1 = 0
-1 + -3ln + 1lny + -1nL + 2nyL = 0 + nL + -1nL + -2nyL + 2nyL
-1 + -3ln + 1lny + -1nL + 2nyL = nL + -1nL + -2nyL + 2nyL

Combine like terms: nL + -1nL = 0
-1 + -3ln + 1lny + -1nL + 2nyL = 0 + -2nyL + 2nyL
-1 + -3ln + 1lny + -1nL + 2nyL = -2nyL + 2nyL

Combine like terms: -2nyL + 2nyL = 0
-1 + -3ln + 1lny + -1nL + 2nyL = 0

The solution to this equation could not be determined.

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