5e^4x+3=30

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Solution for 5e^4x+3=30 equation:


Simplifying
5e4x + 3 = 30

Reorder the terms:
3 + 5e4x = 30

Solving
3 + 5e4x = 30

Solving for variable 'e'.

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

Add '-3' to each side of the equation.
3 + -3 + 5e4x = 30 + -3

Combine like terms: 3 + -3 = 0
0 + 5e4x = 30 + -3
5e4x = 30 + -3

Combine like terms: 30 + -3 = 27
5e4x = 27

Divide each side by '5x'.
e4 = 5.4x-1

Simplifying
e4 = 5.4x-1

Combine like terms: 5.4x-1 + -5.4x-1 = 0.0
e4 + -5.4x-1 = 0.0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e4x + -5.4) = 0.0

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 + -5.4)' equal to zero and attempt to solve: Simplifying e4x + -5.4 = 0 Reorder the terms: -5.4 + e4x = 0 Solving -5.4 + e4x = 0 Move all terms containing e to the left, all other terms to the right. Add '5.4' to each side of the equation. -5.4 + 5.4 + e4x = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + e4x = 0 + 5.4 e4x = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 e4x = 5.4 Divide each side by 'x'. e4 = 5.4x-1 Simplifying e4 = 5.4x-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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