6+0.5e^2x=13

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Solution for 6+0.5e^2x=13 equation: 


Simplifying
6 + 0.5e2x = 13

Solving
6 + 0.5e2x = 13

Solving for variable 'e'.

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

Add '-6' to each side of the equation.
6 + -6 + 0.5e2x = 13 + -6

Combine like terms: 6 + -6 = 0
0 + 0.5e2x = 13 + -6
0.5e2x = 13 + -6

Combine like terms: 13 + -6 = 7
0.5e2x = 7

Divide each side by '0.5x'.
e2 = 14x-1

Simplifying
e2 = 14x-1

Combine like terms: 14x-1 + -14x-1 = 0
e2 + -14x-1 = 0

Factor out the Greatest Common Factor (GCF), 'x-1'.
x-1(e2x + -14) = 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 '(e2x + -14)' equal to zero and attempt to solve:

Simplifying
e2x + -14 = 0

Reorder the terms:
-14 + e2x = 0

Solving
-14 + e2x = 0

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

Add '14' to each side of the equation.
-14 + 14 + e2x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + e2x = 0 + 14
e2x = 0 + 14

Combine like terms: 0 + 14 = 14
e2x = 14

Divide each side by 'x'.
e2 = 14x-1

Simplifying
e2 = 14x-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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