5x=3x-lnx

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Solution for 5x=3x-lnx equation: 


Simplifying
5x = 3x + -1lnx

Reorder the terms:
5x = -1lnx + 3x

Solving
5x = -1lnx + 3x

Solving for variable 'x'.

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

Add 'lnx' to each side of the equation.
lnx + 5x = -1lnx + lnx + 3x

Combine like terms: -1lnx + lnx = 0
lnx + 5x = 0 + 3x
lnx + 5x = 3x

Add '-3x' to each side of the equation.
lnx + 5x + -3x = 3x + -3x

Combine like terms: 5x + -3x = 2x
lnx + 2x = 3x + -3x

Combine like terms: 3x + -3x = 0
lnx + 2x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(ln + 2) = 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 '(ln + 2)' equal to zero and attempt to solve:

Simplifying
ln + 2 = 0

Reorder the terms:
2 + ln = 0

Solving
2 + ln = 0

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

Add '-2' to each side of the equation.
2 + -2 + ln = 0 + -2

Combine like terms: 2 + -2 = 0
0 + ln = 0 + -2
ln = 0 + -2

Combine like terms: 0 + -2 = -2
ln = -2

Add '-1ln' to each side of the equation.
ln + -1ln = -2 + -1ln

Combine like terms: ln + -1ln = 0
0 = -2 + -1ln

Simplifying
0 = -2 + -1ln

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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