10(1-e^3k)=5

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Solution for 10(1-e^3k)=5 equation: 


Simplifying
10(1 + -1e3k) = 5
(1 * 10 + -1e3k * 10) = 5
(10 + -10e3k) = 5

Solving
10 + -10e3k = 5

Solving for variable 'e'.

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

Add '-10' to each side of the equation.
10 + -10 + -10e3k = 5 + -10

Combine like terms: 10 + -10 = 0
0 + -10e3k = 5 + -10
-10e3k = 5 + -10

Combine like terms: 5 + -10 = -5
-10e3k = -5

Divide each side by '-10k'.
e3 = 0.5k-1

Simplifying
e3 = 0.5k-1

Combine like terms: 0.5k-1 + -0.5k-1 = 0.0
e3 + -0.5k-1 = 0.0

Factor out the Greatest Common Factor (GCF), 'k-1'.
k-1(e3k + -0.5) = 0.0


Subproblem 1
Set the factor 'k-1' equal to zero and attempt to solve:

Simplifying
k-1 = 0

Solving
k-1 = 0

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

Add '-1k-1' to each side of the equation.
k-1 + -1k-1 = 0 + -1k-1
Remove the zero:
0 = -1k-1

Simplifying
0 = -1k-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 '(e3k + -0.5)' equal to zero and attempt to solve:

Simplifying
e3k + -0.5 = 0

Reorder the terms:
-0.5 + e3k = 0

Solving
-0.5 + e3k = 0

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + e3k = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + e3k = 0 + 0.5
e3k = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
e3k = 0.5

Divide each side by 'k'.
e3 = 0.5k-1

Simplifying
e3 = 0.5k-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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