Ln(x^2-12)=lnx

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Solution for Ln(x^2-12)=lnx equation: 


Simplifying
Ln(x2 + -12) = lnx

Reorder the terms:
nL(-12 + x2) = lnx
(-12 * nL + x2 * nL) = lnx
(-12nL + nx2L) = lnx

Solving
-12nL + nx2L = lnx

Solving for variable 'n'.

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

Add '-1lnx' to each side of the equation.
-12nL + -1lnx + nx2L = lnx + -1lnx

Reorder the terms:
-1lnx + -12nL + nx2L = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1lnx + -12nL + nx2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1lx + -12L + x2L) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-1lx + -12L + x2L)' equal to zero and attempt to solve:

Simplifying
-1lx + -12L + x2L = 0

Reorder the terms:
-12L + -1lx + x2L = 0

Solving
-12L + -1lx + x2L = 0

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

Add '12L' to each side of the equation.
-12L + -1lx + 12L + x2L = 0 + 12L

Reorder the terms:
-12L + 12L + -1lx + x2L = 0 + 12L

Combine like terms: -12L + 12L = 0
0 + -1lx + x2L = 0 + 12L
-1lx + x2L = 0 + 12L
Remove the zero:
-1lx + x2L = 12L

Add 'lx' to each side of the equation.
-1lx + lx + x2L = 12L + lx

Combine like terms: -1lx + lx = 0
0 + x2L = 12L + lx
x2L = 12L + lx

Add '-1x2L' to each side of the equation.
x2L + -1x2L = 12L + lx + -1x2L

Combine like terms: x2L + -1x2L = 0
0 = 12L + lx + -1x2L

Simplifying
0 = 12L + lx + -1x2L

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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