6+7e^4x=13

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Solution for 6+7e^4x=13 equation: 


Simplifying
6 + 7e4x = 13

Solving
6 + 7e4x = 13

Solving for variable 'e'.

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

Add '-6' to each side of the equation.
6 + -6 + 7e4x = 13 + -6

Combine like terms: 6 + -6 = 0
0 + 7e4x = 13 + -6
7e4x = 13 + -6

Combine like terms: 13 + -6 = 7
7e4x = 7

Divide each side by '7x'.
e4 = x-1

Simplifying
e4 = x-1

Combine like terms: x-1 + -1x-1 = 0
e4 + -1x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e4x + -1) = 0


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

Simplifying
x-1 = 0

Solving
x-1 = 0

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

Add '-1x-1' to each side of the equation.
x-1 + -1x-1 = 0 + -1x-1
Remove the zero:
0 = -1x-1

Simplifying
0 = -1x-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 '(e4x + -1)' equal to zero and attempt to solve:

Simplifying
e4x + -1 = 0

Reorder the terms:
-1 + e4x = 0

Solving
-1 + e4x = 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 + e4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + e4x = 0 + 1
e4x = 0 + 1

Combine like terms: 0 + 1 = 1
e4x = 1

Divide each side by 'x'.
e4 = x-1

Simplifying
e4 = x-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.

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