lny=ln[ln(ax^2+bx+c)]

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Solution for lny=ln[ln(ax^2+bx+c)] equation: 


Simplifying
lny = ln[ln(ax2 + bx + c)]
lny = ln[(ax2 * ln + bx * ln + c * ln)]
lny = ln[(alnx2 + blnx + cln)]
lny = [alnx2 * ln + blnx * ln + cln * ln]
lny = [al2n2x2 + bl2n2x + cl2n2]

Solving
lny = al2n2x2 + bl2n2x + cl2n2

Solving for variable 'l'.

Reorder the terms:
-1al2n2x2 + -1bl2n2x + -1cl2n2 + lny = al2n2x2 + bl2n2x + cl2n2 + -1al2n2x2 + -1bl2n2x + -1cl2n2

Reorder the terms:
-1al2n2x2 + -1bl2n2x + -1cl2n2 + lny = al2n2x2 + -1al2n2x2 + bl2n2x + -1bl2n2x + cl2n2 + -1cl2n2

Combine like terms: al2n2x2 + -1al2n2x2 = 0
-1al2n2x2 + -1bl2n2x + -1cl2n2 + lny = 0 + bl2n2x + -1bl2n2x + cl2n2 + -1cl2n2
-1al2n2x2 + -1bl2n2x + -1cl2n2 + lny = bl2n2x + -1bl2n2x + cl2n2 + -1cl2n2

Combine like terms: bl2n2x + -1bl2n2x = 0
-1al2n2x2 + -1bl2n2x + -1cl2n2 + lny = 0 + cl2n2 + -1cl2n2
-1al2n2x2 + -1bl2n2x + -1cl2n2 + lny = cl2n2 + -1cl2n2

Combine like terms: cl2n2 + -1cl2n2 = 0
-1al2n2x2 + -1bl2n2x + -1cl2n2 + lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1alnx2 + -1blnx + -1cln + y) = 0


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

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-1alnx2 + -1blnx + -1cln + y)' equal to zero and attempt to solve:

Simplifying
-1alnx2 + -1blnx + -1cln + y = 0

Solving
-1alnx2 + -1blnx + -1cln + y = 0

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

Add '-1y' to each side of the equation.
-1alnx2 + -1blnx + -1cln + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-1alnx2 + -1blnx + -1cln + 0 = 0 + -1y
-1alnx2 + -1blnx + -1cln = 0 + -1y
Remove the zero:
-1alnx2 + -1blnx + -1cln = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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