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

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


Simplifying
ln(e6) + -1ln(e2) = 0

Multiply ln * e6
e6ln + -1ln(e2) = 0

Multiply ln * e2
e6ln + -1e2ln = 0

Reorder the terms:
-1e2ln + e6ln = 0

Solving
-1e2ln + e6ln = 0

Solving for variable 'e'.

Factor out the Greatest Common Factor (GCF), 'e2ln'.
e2ln(-1 + e4) = 0

Factor a difference between two squares.
e2ln((1 + e2)(-1 + e2)) = 0

Factor a difference between two squares.
e2ln((1 + e2)((1 + e)(-1 + e))) = 0


Subproblem 1
Set the factor 'e2ln' equal to zero and attempt to solve:

Simplifying
e2ln = 0

Solving
e2ln = 0

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

Simplifying
e2ln = 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 + e2)' equal to zero and attempt to solve:

Simplifying
1 + e2 = 0

Solving
1 + e2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + e2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + e2 = 0 + -1
e2 = 0 + -1

Combine like terms: 0 + -1 = -1
e2 = -1

Simplifying
e2 = -1

The solution to this equation could not be determined.

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

Subproblem 3
Set the factor '(1 + e)' equal to zero and attempt to solve:

Simplifying
1 + e = 0

Solving
1 + e = 0

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

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

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

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

Simplifying
e = -1

Subproblem 4
Set the factor '(-1 + e)' equal to zero and attempt to solve:

Simplifying
-1 + e = 0

Solving
-1 + e = 0

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

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

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

Combine like terms: 0 + 1 = 1
e = 1

Simplifying
e = 1
Solution
e = {-1, 1}

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