6=e^4t

Solution for 6=e^4t equation:

Simplifying
6 = e4t

Solving
6 = e4t

Solving for variable 'e'.

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

Add '-1e4t' to each side of the equation.
6 + -1e4t = e4t + -1e4t

Combine like terms: e4t + -1e4t = 0
6 + -1e4t = 0

Add '-6' to each side of the equation.
6 + -6 + -1e4t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1e4t = 0 + -6
-1e4t = 0 + -6

Combine like terms: 0 + -6 = -6
-1e4t = -6

Divide each side by '-1t'.
e4 = 6t-1

Simplifying
e4 = 6t-1

Combine like terms: 6t-1 + -6t-1 = 0
e4 + -6t-1 = 0

Factor out the Greatest Common Factor (GCF), 't-1'.
t-1(e4t + -6) = 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 + -6)' equal to zero and attempt to solve:

Simplifying
e4t + -6 = 0

Reorder the terms:
-6 + e4t = 0

Solving
-6 + e4t = 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 + e4t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + e4t = 0 + 6
e4t = 0 + 6

Combine like terms: 0 + 6 = 6
e4t = 6

Divide each side by 't'.
e4 = 6t-1

Simplifying
e4 = 6t-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.