e^4x=e

Solution for e^4x=e equation:

Simplifying
e4x = e

Solving
e4x = e

Solving for variable 'e'.

Reorder the terms:
-1e + e4x = e + -1e

Combine like terms: e + -1e = 0
-1e + e4x = 0

Factor out the Greatest Common Factor (GCF), 'e'.
e(-1 + e3x) = 0

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

Simplifying
e = 0

Solving
e = 0

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

Simplifying
e = 0
Subproblem 2
Set the factor '(-1 + e3x)' equal to zero and attempt to solve:

Simplifying
-1 + e3x = 0

Solving
-1 + e3x = 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 + e3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + e3x = 0 + 1
e3x = 0 + 1

Combine like terms: 0 + 1 = 1
e3x = 1

Divide each side by 'x'.
e3 = x-1

Simplifying
e3 = x-1

The solution to this equation could not be determined.

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