e^4x=5

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Solution for e^4x=5 equation:


Simplifying
e4x = 5

Solving
e4x = 5

Solving for variable 'e'.

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

Divide each side by 'x'.
e4 = 5x-1

Simplifying
e4 = 5x-1

Combine like terms: 5x-1 + -5x-1 = 0
e4 + -5x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e4x + -5) = 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 '(e4x + -5)' equal to zero and attempt to solve: Simplifying e4x + -5 = 0 Reorder the terms: -5 + e4x = 0 Solving -5 + e4x = 0 Move all terms containing e to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + e4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + e4x = 0 + 5 e4x = 0 + 5 Combine like terms: 0 + 5 = 5 e4x = 5 Divide each side by 'x'. e4 = 5x-1 Simplifying e4 = 5x-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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