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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