n(y)=ln(ax^2+b)

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Solution for n(y)=ln(ax^2+b) equation: 


Simplifying
n(y) = ln(ax2 + b)

Multiply n * y
ny = ln(ax2 + b)
ny = (ax2 * ln + b * ln)
ny = (alnx2 + bln)

Solving
ny = alnx2 + bln

Solving for variable 'n'.

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

Add '-1alnx2' to each side of the equation.
-1alnx2 + ny = alnx2 + -1alnx2 + bln

Combine like terms: alnx2 + -1alnx2 = 0
-1alnx2 + ny = 0 + bln
-1alnx2 + ny = bln

Add '-1bln' to each side of the equation.
-1alnx2 + -1bln + ny = bln + -1bln

Combine like terms: bln + -1bln = 0
-1alnx2 + -1bln + ny = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1alx2 + -1bl + y) = 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 '(-1alx2 + -1bl + y)' equal to zero and attempt to solve:

Simplifying
-1alx2 + -1bl + y = 0

Solving
-1alx2 + -1bl + y = 0

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

Add 'alx2' to each side of the equation.
-1alx2 + -1bl + alx2 + y = 0 + alx2

Reorder the terms:
-1alx2 + alx2 + -1bl + y = 0 + alx2

Combine like terms: -1alx2 + alx2 = 0
0 + -1bl + y = 0 + alx2
-1bl + y = 0 + alx2
Remove the zero:
-1bl + y = alx2

Add 'bl' to each side of the equation.
-1bl + bl + y = alx2 + bl

Combine like terms: -1bl + bl = 0
0 + y = alx2 + bl
y = alx2 + bl

Add '-1y' to each side of the equation.
y + -1y = alx2 + bl + -1y

Combine like terms: y + -1y = 0
0 = alx2 + bl + -1y

Simplifying
0 = alx2 + bl + -1y

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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