3+7e^2x=10

Solution for 3+7e^2x=10 equation:

Simplifying
3 + 7e2x = 10

Solving
3 + 7e2x = 10

Solving for variable 'e'.

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

Add '-3' to each side of the equation.
3 + -3 + 7e2x = 10 + -3

Combine like terms: 3 + -3 = 0
0 + 7e2x = 10 + -3
7e2x = 10 + -3

Combine like terms: 10 + -3 = 7
7e2x = 7

Divide each side by '7x'.
e2 = x-1

Simplifying
e2 = x-1

Combine like terms: x-1 + -1x-1 = 0
e2 + -1x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -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 '(e2x + -1)' equal to zero and attempt to solve:

Simplifying
e2x + -1 = 0

Reorder the terms:
-1 + e2x = 0

Solving
-1 + e2x = 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 + e2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + e2x = 0 + 1
e2x = 0 + 1

Combine like terms: 0 + 1 = 1
e2x = 1

Divide each side by 'x'.
e2 = x-1

Simplifying
e2 = 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.