ln(x^2-2)=ln(x-2)

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Solution for ln(x^2-2)=ln(x-2) equation: 


Simplifying
ln(x2 + -2) = ln(x + -2)

Reorder the terms:
ln(-2 + x2) = ln(x + -2)
(-2 * ln + x2 * ln) = ln(x + -2)
(-2ln + lnx2) = ln(x + -2)

Reorder the terms:
-2ln + lnx2 = ln(-2 + x)
-2ln + lnx2 = (-2 * ln + x * ln)
-2ln + lnx2 = (-2ln + lnx)

Add '2ln' to each side of the equation.
-2ln + 2ln + lnx2 = -2ln + 2ln + lnx

Combine like terms: -2ln + 2ln = 0
0 + lnx2 = -2ln + 2ln + lnx
lnx2 = -2ln + 2ln + lnx

Combine like terms: -2ln + 2ln = 0
lnx2 = 0 + lnx
lnx2 = lnx

Solving
lnx2 = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
-1lnx + lnx2 = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1lnx + lnx2 = 0

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


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

Simplifying
lnx = 0

Solving
lnx = 0

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

Simplifying
lnx = 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 l 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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