E^2x=65e^5x

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Solution for E^2x=65e^5x equation:


Simplifying
E2x = 65e5x

Solving
xE2 = 65e5x

Solving for variable 'x'.

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

Add '-65e5x' to each side of the equation.
-65e5x + xE2 = 65e5x + -65e5x

Combine like terms: 65e5x + -65e5x = 0
-65e5x + xE2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-65e5 + E2) = 0

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 '(-65e5 + E2)' equal to zero and attempt to solve: Simplifying -65e5 + E2 = 0 Reorder the terms: E2 + -65e5 = 0 Solving E2 + -65e5 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1E2' to each side of the equation. E2 + -1E2 + -65e5 = 0 + -1E2 Combine like terms: E2 + -1E2 = 0 0 + -65e5 = 0 + -1E2 -65e5 = 0 + -1E2 Remove the zero: -65e5 = -1E2 Add '65e5' to each side of the equation. -65e5 + 65e5 = -1E2 + 65e5 Combine like terms: -65e5 + 65e5 = 0 0 = -1E2 + 65e5 Simplifying 0 = -1E2 + 65e5 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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