4+e^2x+1=8

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Solution for 4+e^2x+1=8 equation:


Simplifying
4 + e2x + 1 = 8

Reorder the terms:
4 + 1 + e2x = 8

Combine like terms: 4 + 1 = 5
5 + e2x = 8

Solving
5 + e2x = 8

Solving for variable 'e'.

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 = 8 + -5

Combine like terms: 5 + -5 = 0
0 + e2x = 8 + -5
e2x = 8 + -5

Combine like terms: 8 + -5 = 3
e2x = 3

Divide each side by 'x'.
e2 = 3x-1

Simplifying
e2 = 3x-1

Combine like terms: 3x-1 + -3x-1 = 0
e2 + -3x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -3) = 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 + -3)' equal to zero and attempt to solve: Simplifying e2x + -3 = 0 Reorder the terms: -3 + e2x = 0 Solving -3 + e2x = 0 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 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + e2x = 0 + 3 e2x = 0 + 3 Combine like terms: 0 + 3 = 3 e2x = 3 Divide each side by 'x'. e2 = 3x-1 Simplifying e2 = 3x-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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