e^3x=e^5x

Solution for e^3x=e^5x equation:

Simplifying
e3x = e5x

Solving
e3x = e5x

Solving for variable 'e'.

Combine like terms: e5x + -1e5x = 0
e3x + -1e5x = 0

Factor out the Greatest Common Factor (GCF), 'e3x'.
e3x(1 + -1e2) = 0

Factor a difference between two squares.
e3x((1 + e)(1 + -1e)) = 0

Subproblem 1
Set the factor 'e3x' equal to zero and attempt to solve:

Simplifying
e3x = 0

Solving
e3x = 0

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

Simplifying
e3x = 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 + 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 3
Set the factor '(1 + -1e)' equal to zero and attempt to solve:

Simplifying
1 + -1e = 0

Solving
1 + -1e = 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 + -1e = 0 + -1

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

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

Divide each side by '-1'.
e = 1

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