5e^4(x)+2=16

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Solution for 5e^4(x)+2=16 equation: 


Simplifying
5e4(x) + 2 = 16

Multiply e4 * x
5e4x + 2 = 16

Reorder the terms:
2 + 5e4x = 16

Solving
2 + 5e4x = 16

Solving for variable 'e'.

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

Add '-2' to each side of the equation.
2 + -2 + 5e4x = 16 + -2

Combine like terms: 2 + -2 = 0
0 + 5e4x = 16 + -2
5e4x = 16 + -2

Combine like terms: 16 + -2 = 14
5e4x = 14

Divide each side by '5x'.
e4 = 2.8x-1

Simplifying
e4 = 2.8x-1

Combine like terms: 2.8x-1 + -2.8x-1 = 0.0
e4 + -2.8x-1 = 0.0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e4x + -2.8) = 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 + -2.8)' equal to zero and attempt to solve:

Simplifying
e4x + -2.8 = 0

Reorder the terms:
-2.8 + e4x = 0

Solving
-2.8 + e4x = 0

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

Add '2.8' to each side of the equation.
-2.8 + 2.8 + e4x = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + e4x = 0 + 2.8
e4x = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
e4x = 2.8

Divide each side by 'x'.
e4 = 2.8x-1

Simplifying
e4 = 2.8x-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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