Ln(2x+1)+(x-3)-2lnx=0

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Solution for Ln(2x+1)+(x-3)-2lnx=0 equation: 


Simplifying
Ln(2x + 1) + (x + -3) + -2lnx = 0

Reorder the terms:
nL(1 + 2x) + (x + -3) + -2lnx = 0
(1 * nL + 2x * nL) + (x + -3) + -2lnx = 0
(1nL + 2nxL) + (x + -3) + -2lnx = 0

Reorder the terms:
1nL + 2nxL + (-3 + x) + -2lnx = 0

Remove parenthesis around (-3 + x)
1nL + 2nxL + -3 + x + -2lnx = 0

Reorder the terms:
-3 + -2lnx + 1nL + 2nxL + x = 0

Solving
-3 + -2lnx + 1nL + 2nxL + x = 0

Solving for variable 'l'.

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

Add '3' to each side of the equation.
-3 + -2lnx + 1nL + 2nxL + 3 + x = 0 + 3

Reorder the terms:
-3 + 3 + -2lnx + 1nL + 2nxL + x = 0 + 3

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

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

Add '-1nL' to each side of the equation.
-2lnx + 1nL + 2nxL + -1nL + x = 3 + -1nL

Reorder the terms:
-2lnx + 1nL + -1nL + 2nxL + x = 3 + -1nL

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

Add '-2nxL' to each side of the equation.
-2lnx + 2nxL + -2nxL + x = 3 + -1nL + -2nxL

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

Add '-1x' to each side of the equation.
-2lnx + x + -1x = 3 + -1nL + -2nxL + -1x

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

Divide each side by '-2nx'.
l = -1.5n-1x-1 + 0.5x-1L + L + 0.5n-1

Simplifying
l = -1.5n-1x-1 + 0.5x-1L + L + 0.5n-1

Reorder the terms:
l = L + 0.5n-1 + -1.5n-1x-1 + 0.5x-1L

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