6e^2x=7e^4x

Solution for 6e^2x=7e^4x equation:

Simplifying
6e2x = 7e4x

Solving
6e2x = 7e4x

Solving for variable 'e'.

Combine like terms: 7e4x + -7e4x = 0
6e2x + -7e4x = 0

Factor out the Greatest Common Factor (GCF), 'e2x'.
e2x(6 + -7e2) = 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 '(6 + -7e2)' equal to zero and attempt to solve:

Simplifying
6 + -7e2 = 0

Solving
6 + -7e2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7e2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7e2 = 0 + -6
-7e2 = 0 + -6

Combine like terms: 0 + -6 = -6
-7e2 = -6

Divide each side by '-7'.
e2 = 0.8571428571

Simplifying
e2 = 0.8571428571

Take the square root of each side:
e = {-0.9258201, 0.9258201}
Solution
e = {-0.9258201, 0.9258201}