3e^2x=5e^4x

Solution for 3e^2x=5e^4x equation:

Simplifying
3e2x = 5e4x

Solving
3e2x = 5e4x

Solving for variable 'e'.

Combine like terms: 5e4x + -5e4x = 0
3e2x + -5e4x = 0

Factor out the Greatest Common Factor (GCF), 'e2x'.
e2x(3 + -5e2) = 0

Subproblem 1
Set the factor 'e2x' equal to zero and attempt to solve:

Simplifying
e2x = 0

Solving
e2x = 0

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

Simplifying
e2x = 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 '(3 + -5e2)' equal to zero and attempt to solve:

Simplifying
3 + -5e2 = 0

Solving
3 + -5e2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5e2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5e2 = 0 + -3
-5e2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5e2 = -3

Divide each side by '-5'.
e2 = 0.6

Simplifying
e2 = 0.6

Take the square root of each side:
e = {-0.774596669, 0.774596669}
Solution
e = {-0.774596669, 0.774596669}