Lnu=-lnx

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Solution for Lnu=-lnx equation:


Simplifying
Lnu = -1lnx

Solving
nuL = -1lnx

Solving for variable 'n'.

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

Add 'lnx' to each side of the equation.
lnx + nuL = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
lnx + nuL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(lx + uL) = 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 '(lx + uL)' equal to zero and attempt to solve: Simplifying lx + uL = 0 Solving lx + uL = 0 Move all terms containing n to the left, all other terms to the right. Add '-1lx' to each side of the equation. lx + -1lx + uL = 0 + -1lx Combine like terms: lx + -1lx = 0 0 + uL = 0 + -1lx uL = 0 + -1lx Remove the zero: uL = -1lx Add '-1uL' to each side of the equation. uL + -1uL = -1lx + -1uL Combine like terms: uL + -1uL = 0 0 = -1lx + -1uL Simplifying 0 = -1lx + -1uL 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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