e^2x-3=7

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Solution for e^2x-3=7 equation: 


Simplifying
e2x + -3 = 7

Reorder the terms:
-3 + e2x = 7

Solving
-3 + e2x = 7

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 + e2x = 7 + 3

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

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

Divide each side by 'x'.
e2 = 10x-1

Simplifying
e2 = 10x-1

Combine like terms: 10x-1 + -10x-1 = 0
e2 + -10x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -10) = 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 + -10)' equal to zero and attempt to solve:

Simplifying
e2x + -10 = 0

Reorder the terms:
-10 + e2x = 0

Solving
-10 + e2x = 0

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

Add '10' to each side of the equation.
-10 + 10 + e2x = 0 + 10

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

Combine like terms: 0 + 10 = 10
e2x = 10

Divide each side by 'x'.
e2 = 10x-1

Simplifying
e2 = 10x-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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