(e^2x)-7=-2

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Solution for (e^2x)-7=-2 equation: 


Simplifying
(e2x) + -7 = -2
e2x + -7 = -2

Reorder the terms:
-7 + e2x = -2

Solving
-7 + e2x = -2

Solving for variable 'e'.

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

Add '7' to each side of the equation.
-7 + 7 + e2x = -2 + 7

Combine like terms: -7 + 7 = 0
0 + e2x = -2 + 7
e2x = -2 + 7

Combine like terms: -2 + 7 = 5
e2x = 5

Divide each side by 'x'.
e2 = 5x-1

Simplifying
e2 = 5x-1

Combine like terms: 5x-1 + -5x-1 = 0
e2 + -5x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -5) = 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 + -5)' equal to zero and attempt to solve:

Simplifying
e2x + -5 = 0

Reorder the terms:
-5 + e2x = 0

Solving
-5 + e2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + e2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + e2x = 0 + 5
e2x = 0 + 5

Combine like terms: 0 + 5 = 5
e2x = 5

Divide each side by 'x'.
e2 = 5x-1

Simplifying
e2 = 5x-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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