Ln(x-2)+Ln(2x+3)=2Lnx

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Solution for Ln(x-2)+Ln(2x+3)=2Lnx equation: 


Simplifying
Ln(x + -2) + Ln(2x + 3) = 2Lnx

Reorder the terms:
nL(-2 + x) + Ln(2x + 3) = 2Lnx
(-2 * nL + x * nL) + Ln(2x + 3) = 2Lnx
(-2nL + nxL) + Ln(2x + 3) = 2Lnx

Reorder the terms:
-2nL + nxL + nL(3 + 2x) = 2Lnx
-2nL + nxL + (3 * nL + 2x * nL) = 2Lnx
-2nL + nxL + (3nL + 2nxL) = 2Lnx

Reorder the terms:
-2nL + 3nL + nxL + 2nxL = 2Lnx

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

Combine like terms: nxL + 2nxL = 3nxL
1nL + 3nxL = 2Lnx

Solving
1nL + 3nxL = 2nxL

Solving for variable 'n'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'nL'.
nL(1 + x) = 0


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

Simplifying
nL = 0

Solving
nL = 0

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

Simplifying
nL = 0

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Add '-1x' to each side of the equation.
x + -1x = -1 + -1x

Combine like terms: x + -1x = 0
0 = -1 + -1x

Simplifying
0 = -1 + -1x

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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