Ln(2x-1)-ln(x-1)=2

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


Simplifying
Ln(2x + -1) + -1ln(x + -1) = 2

Reorder the terms:
nL(-1 + 2x) + -1ln(x + -1) = 2
(-1 * nL + 2x * nL) + -1ln(x + -1) = 2
(-1nL + 2nxL) + -1ln(x + -1) = 2

Reorder the terms:
-1nL + 2nxL + -1ln(-1 + x) = 2
-1nL + 2nxL + (-1 * -1ln + x * -1ln) = 2
-1nL + 2nxL + (1ln + -1lnx) = 2

Reorder the terms:
1ln + -1lnx + -1nL + 2nxL = 2

Solving
1ln + -1lnx + -1nL + 2nxL = 2

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.
1ln + -1lnx + -1nL + nL + 2nxL = 2 + nL

Combine like terms: -1nL + nL = 0
1ln + -1lnx + 0 + 2nxL = 2 + nL
1ln + -1lnx + 2nxL = 2 + nL

Add '-2nxL' to each side of the equation.
1ln + -1lnx + 2nxL + -2nxL = 2 + nL + -2nxL

Combine like terms: 2nxL + -2nxL = 0
1ln + -1lnx + 0 = 2 + nL + -2nxL
1ln + -1lnx = 2 + nL + -2nxL

Reorder the terms:
-2 + 1ln + -1lnx + -1nL + 2nxL = 2 + nL + -2nxL + -2 + -1nL + 2nxL

Reorder the terms:
-2 + 1ln + -1lnx + -1nL + 2nxL = 2 + -2 + nL + -1nL + -2nxL + 2nxL

Combine like terms: 2 + -2 = 0
-2 + 1ln + -1lnx + -1nL + 2nxL = 0 + nL + -1nL + -2nxL + 2nxL
-2 + 1ln + -1lnx + -1nL + 2nxL = nL + -1nL + -2nxL + 2nxL

Combine like terms: nL + -1nL = 0
-2 + 1ln + -1lnx + -1nL + 2nxL = 0 + -2nxL + 2nxL
-2 + 1ln + -1lnx + -1nL + 2nxL = -2nxL + 2nxL

Combine like terms: -2nxL + 2nxL = 0
-2 + 1ln + -1lnx + -1nL + 2nxL = 0

The solution to this equation could not be determined.

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