2e^4t-1=5

Solution for 2e^4t-1=5 equation:

Simplifying
2e4t + -1 = 5

Reorder the terms:
-1 + 2e4t = 5

Solving
-1 + 2e4t = 5

Solving for variable 'e'.

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

Add '1' to each side of the equation.
-1 + 1 + 2e4t = 5 + 1

Combine like terms: -1 + 1 = 0
0 + 2e4t = 5 + 1
2e4t = 5 + 1

Combine like terms: 5 + 1 = 6
2e4t = 6

Divide each side by '2t'.
e4 = 3t-1

Simplifying
e4 = 3t-1

Combine like terms: 3t-1 + -3t-1 = 0
e4 + -3t-1 = 0

Factor out the Greatest Common Factor (GCF), 't-1'.
t-1(e4t + -3) = 0

Subproblem 1
Set the factor 't-1' equal to zero and attempt to solve:

Simplifying
t-1 = 0

Solving
t-1 = 0

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

Add '-1t-1' to each side of the equation.
t-1 + -1t-1 = 0 + -1t-1
Remove the zero:
0 = -1t-1

Simplifying
0 = -1t-1

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 '(e4t + -3)' equal to zero and attempt to solve:

Simplifying
e4t + -3 = 0

Reorder the terms:
-3 + e4t = 0

Solving
-3 + e4t = 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 + e4t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + e4t = 0 + 3
e4t = 0 + 3

Combine like terms: 0 + 3 = 3
e4t = 3

Divide each side by 't'.
e4 = 3t-1

Simplifying
e4 = 3t-1

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.