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

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


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

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

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

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

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

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

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

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

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

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

Solving for variable 'l'.

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

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

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

Combine like terms: -1lnx + -2lnx = -3lnx
-3lnx + -1nL + nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-3lnx + -1nL + nxL = 0

Add 'nL' to each side of the equation.
-3lnx + -1nL + nL + nxL = 0 + nL

Combine like terms: -1nL + nL = 0
-3lnx + 0 + nxL = 0 + nL
-3lnx + nxL = 0 + nL
Remove the zero:
-3lnx + nxL = nL

Add '-1nxL' to each side of the equation.
-3lnx + nxL + -1nxL = nL + -1nxL

Combine like terms: nxL + -1nxL = 0
-3lnx + 0 = nL + -1nxL
-3lnx = nL + -1nxL

Divide each side by '-3nx'.
l = -0.3333333333x-1L + 0.3333333333L

Simplifying
l = -0.3333333333x-1L + 0.3333333333L

Reorder the terms:
l = 0.3333333333L + -0.3333333333x-1L

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