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

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


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

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

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

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

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

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

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.
-3ln + -1lnx + 1nL + -1nL + 2nxL = 0 + -1nL

Combine like terms: 1nL + -1nL = 0
-3ln + -1lnx + 0 + 2nxL = 0 + -1nL
-3ln + -1lnx + 2nxL = 0 + -1nL
Remove the zero:
-3ln + -1lnx + 2nxL = -1nL

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3l + -1lx + L + 2xL) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-3l + -1lx + L + 2xL)' equal to zero and attempt to solve:

Simplifying
-3l + -1lx + L + 2xL = 0

Reorder the terms:
L + -3l + -1lx + 2xL = 0

Solving
L + -3l + -1lx + 2xL = 0

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

Add '-1L' to each side of the equation.
L + -3l + -1lx + -1L + 2xL = 0 + -1L

Reorder the terms:
L + -1L + -3l + -1lx + 2xL = 0 + -1L

Combine like terms: L + -1L = 0
0 + -3l + -1lx + 2xL = 0 + -1L
-3l + -1lx + 2xL = 0 + -1L
Remove the zero:
-3l + -1lx + 2xL = -1L

Add '-2xL' to each side of the equation.
-3l + -1lx + 2xL + -2xL = -1L + -2xL

Combine like terms: 2xL + -2xL = 0
-3l + -1lx + 0 = -1L + -2xL
-3l + -1lx = -1L + -2xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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