ln(x^2-2)=ln(6)

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Solution for ln(x^2-2)=ln(6) equation: 


Simplifying
ln(x2 + -2) = ln(6)

Reorder the terms:
ln(-2 + x2) = ln(6)
(-2 * ln + x2 * ln) = ln(6)
(-2ln + lnx2) = ln(6)

Reorder the terms for easier multiplication:
-2ln + lnx2 = 6ln

Solving
-2ln + lnx2 = 6ln

Solving for variable 'l'.

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

Add '-6ln' to each side of the equation.
-2ln + -6ln + lnx2 = 6ln + -6ln

Combine like terms: -2ln + -6ln = -8ln
-8ln + lnx2 = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-8ln + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-8 + x2) = 0


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

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 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 '(-8 + x2)' equal to zero and attempt to solve:

Simplifying
-8 + x2 = 0

Solving
-8 + x2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x2 = 0 + 8
x2 = 0 + 8

Combine like terms: 0 + 8 = 8
x2 = 8

Add '-1x2' to each side of the equation.
x2 + -1x2 = 8 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 8 + -1x2

Simplifying
0 = 8 + -1x2

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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