5x=5e^8x

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Solution for 5x=5e^8x equation:


Simplifying
5x = 5e8x

Solving
5x = 5e8x

Solving for variable 'x'.

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

Add '-5e8x' to each side of the equation.
-5e8x + 5x = 5e8x + -5e8x

Combine like terms: 5e8x + -5e8x = 0
-5e8x + 5x = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-1e8 + 1) = 0

Factor a difference between two squares.
5x((e4 + 1)(-1e4 + 1)) = 0

Factor a difference between two squares.
5x((e4 + 1)((e2 + 1)(-1e2 + 1))) = 0

Factor a difference between two squares.
5x((e4 + 1)((e2 + 1)((e + 1)(-1e + 1)))) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(e4 + 1)' equal to zero and attempt to solve: Simplifying e4 + 1 = 0 Reorder the terms: 1 + e4 = 0 Solving 1 + e4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + e4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + e4 = 0 + -1 e4 = 0 + -1 Combine like terms: 0 + -1 = -1 e4 = -1 Add '-1e4' to each side of the equation. e4 + -1e4 = -1 + -1e4 Combine like terms: e4 + -1e4 = 0 0 = -1 + -1e4 Simplifying 0 = -1 + -1e4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(e2 + 1)' equal to zero and attempt to solve: Simplifying e2 + 1 = 0 Reorder the terms: 1 + e2 = 0 Solving 1 + e2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + e2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + e2 = 0 + -1 e2 = 0 + -1 Combine like terms: 0 + -1 = -1 e2 = -1 Add '-1e2' to each side of the equation. e2 + -1e2 = -1 + -1e2 Combine like terms: e2 + -1e2 = 0 0 = -1 + -1e2 Simplifying 0 = -1 + -1e2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 4

Set the factor '(e + 1)' equal to zero and attempt to solve: Simplifying e + 1 = 0 Reorder the terms: 1 + e = 0 Solving 1 + e = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + e = 0 + -1 Combine like terms: 1 + -1 = 0 0 + e = 0 + -1 e = 0 + -1 Combine like terms: 0 + -1 = -1 e = -1 Add '-1e' to each side of the equation. e + -1e = -1 + -1e Combine like terms: e + -1e = 0 0 = -1 + -1e Simplifying 0 = -1 + -1e The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 5

Set the factor '(-1e + 1)' equal to zero and attempt to solve: Simplifying -1e + 1 = 0 Reorder the terms: 1 + -1e = 0 Solving 1 + -1e = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1e = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1e = 0 + -1 -1e = 0 + -1 Combine like terms: 0 + -1 = -1 -1e = -1 Add 'e' to each side of the equation. -1e + e = -1 + e Combine like terms: -1e + e = 0 0 = -1 + e Simplifying 0 = -1 + e The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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