2lnx-2lnx+31n=5lnx-lnx+2ln

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Solution for 2lnx-2lnx+31n=5lnx-lnx+2ln equation: 


Simplifying
2lnx + -2lnx + 31n = 5lnx + -1lnx + 2ln

Combine like terms: 2lnx + -2lnx = 0
0 + 31n = 5lnx + -1lnx + 2ln
31n = 5lnx + -1lnx + 2ln

Reorder the terms:
31n = 2ln + 5lnx + -1lnx

Combine like terms: 5lnx + -1lnx = 4lnx
31n = 2ln + 4lnx

Solving
31n = 2ln + 4lnx

Solving for variable 'n'.

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

Add '-2ln' to each side of the equation.
-2ln + 31n = 2ln + -2ln + 4lnx

Combine like terms: 2ln + -2ln = 0
-2ln + 31n = 0 + 4lnx
-2ln + 31n = 4lnx

Add '-4lnx' to each side of the equation.
-2ln + -4lnx + 31n = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
-2ln + -4lnx + 31n = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2l + -4lx + 31) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-2l + -4lx + 31)' equal to zero and attempt to solve:

Simplifying
-2l + -4lx + 31 = 0

Reorder the terms:
31 + -2l + -4lx = 0

Solving
31 + -2l + -4lx = 0

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

Add '-31' to each side of the equation.
31 + -2l + -31 + -4lx = 0 + -31

Reorder the terms:
31 + -31 + -2l + -4lx = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -2l + -4lx = 0 + -31
-2l + -4lx = 0 + -31

Combine like terms: 0 + -31 = -31
-2l + -4lx = -31

Add '2l' to each side of the equation.
-2l + 2l + -4lx = -31 + 2l

Combine like terms: -2l + 2l = 0
0 + -4lx = -31 + 2l
-4lx = -31 + 2l

Add '4lx' to each side of the equation.
-4lx + 4lx = -31 + 2l + 4lx

Combine like terms: -4lx + 4lx = 0
0 = -31 + 2l + 4lx

Simplifying
0 = -31 + 2l + 4lx

The solution to this equation could not be determined.

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

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