C(x)=100x-100lnx

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Solution for C(x)=100x-100lnx equation: 


Simplifying
C(x) = 100x + -100lnx

Multiply C * x
xC = 100x + -100lnx

Reorder the terms:
xC = -100lnx + 100x

Solving
xC = -100lnx + 100x

Solving for variable 'x'.

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

Add '100lnx' to each side of the equation.
100lnx + xC = -100lnx + 100lnx + 100x

Combine like terms: -100lnx + 100lnx = 0
100lnx + xC = 0 + 100x
100lnx + xC = 100x

Add '-100x' to each side of the equation.
100lnx + -100x + xC = 100x + -100x

Combine like terms: 100x + -100x = 0
100lnx + -100x + xC = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(100ln + -100 + C) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(100ln + -100 + C)' equal to zero and attempt to solve:

Simplifying
100ln + -100 + C = 0

Reorder the terms:
-100 + C + 100ln = 0

Solving
-100 + C + 100ln = 0

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

Add '100' to each side of the equation.
-100 + C + 100 + 100ln = 0 + 100

Reorder the terms:
-100 + 100 + C + 100ln = 0 + 100

Combine like terms: -100 + 100 = 0
0 + C + 100ln = 0 + 100
C + 100ln = 0 + 100

Combine like terms: 0 + 100 = 100
C + 100ln = 100

Add '-1C' to each side of the equation.
C + -1C + 100ln = 100 + -1C

Combine like terms: C + -1C = 0
0 + 100ln = 100 + -1C
100ln = 100 + -1C

Add '-100ln' to each side of the equation.
100ln + -100ln = 100 + -1C + -100ln

Combine like terms: 100ln + -100ln = 0
0 = 100 + -1C + -100ln

Simplifying
0 = 100 + -1C + -100ln

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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