Ln(2x+1)+ln(x-1)=lnx+8

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Solution for Ln(2x+1)+ln(x-1)=lnx+8 equation: 


Simplifying
Ln(2x + 1) + ln(x + -1) = lnx + 8

Reorder the terms:
nL(1 + 2x) + ln(x + -1) = lnx + 8
(1 * nL + 2x * nL) + ln(x + -1) = lnx + 8
(1nL + 2nxL) + ln(x + -1) = lnx + 8

Reorder the terms:
1nL + 2nxL + ln(-1 + x) = lnx + 8
1nL + 2nxL + (-1 * ln + x * ln) = lnx + 8
1nL + 2nxL + (-1ln + lnx) = lnx + 8

Reorder the terms:
-1ln + lnx + 1nL + 2nxL = lnx + 8

Reorder the terms:
-1ln + lnx + 1nL + 2nxL = 8 + lnx

Add '-1lnx' to each side of the equation.
-1ln + lnx + 1nL + -1lnx + 2nxL = 8 + lnx + -1lnx

Reorder the terms:
-1ln + lnx + -1lnx + 1nL + 2nxL = 8 + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln + 0 + 1nL + 2nxL = 8 + lnx + -1lnx
-1ln + 1nL + 2nxL = 8 + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln + 1nL + 2nxL = 8 + 0
-1ln + 1nL + 2nxL = 8

Solving
-1ln + 1nL + 2nxL = 8

Solving for variable 'l'.

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

Add '-1nL' to each side of the equation.
-1ln + 1nL + -1nL + 2nxL = 8 + -1nL

Combine like terms: 1nL + -1nL = 0
-1ln + 0 + 2nxL = 8 + -1nL
-1ln + 2nxL = 8 + -1nL

Add '-2nxL' to each side of the equation.
-1ln + 2nxL + -2nxL = 8 + -1nL + -2nxL

Combine like terms: 2nxL + -2nxL = 0
-1ln + 0 = 8 + -1nL + -2nxL
-1ln = 8 + -1nL + -2nxL

Divide each side by '-1n'.
l = -8n-1 + L + 2xL

Simplifying
l = -8n-1 + L + 2xL

Reorder the terms:
l = L + -8n-1 + 2xL

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