5*e^2x-1=4

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Solution for 5*e^2x-1=4 equation: 


Simplifying
5e2x + -1 = 4

Reorder the terms:
-1 + 5e2x = 4

Solving
-1 + 5e2x = 4

Solving for variable 'e'.

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

Add '1' to each side of the equation.
-1 + 1 + 5e2x = 4 + 1

Combine like terms: -1 + 1 = 0
0 + 5e2x = 4 + 1
5e2x = 4 + 1

Combine like terms: 4 + 1 = 5
5e2x = 5

Divide each side by '5x'.
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.

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