5e^4x+3=15

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Solution for 5e^4x+3=15 equation: 


Simplifying
5e4x + 3 = 15

Reorder the terms:
3 + 5e4x = 15

Solving
3 + 5e4x = 15

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 = 15 + -3

Combine like terms: 3 + -3 = 0
0 + 5e4x = 15 + -3
5e4x = 15 + -3

Combine like terms: 15 + -3 = 12
5e4x = 12

Divide each side by '5x'.
e4 = 2.4x-1

Simplifying
e4 = 2.4x-1

Combine like terms: 2.4x-1 + -2.4x-1 = 0.0
e4 + -2.4x-1 = 0.0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e4x + -2.4) = 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 + -2.4)' equal to zero and attempt to solve:

Simplifying
e4x + -2.4 = 0

Reorder the terms:
-2.4 + e4x = 0

Solving
-2.4 + e4x = 0

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + e4x = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + e4x = 0 + 2.4
e4x = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
e4x = 2.4

Divide each side by 'x'.
e4 = 2.4x-1

Simplifying
e4 = 2.4x-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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