ln(y)=ln(ax^2+bx+c)

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Solution for ln(y)=ln(ax^2+bx+c) equation:


Simplifying
ln(y) = ln(ax2 + bx + c)

Multiply ln * y
lny = ln(ax2 + bx + c)
lny = (ax2 * ln + bx * ln + c * ln)
lny = (alnx2 + blnx + cln)

Solving
lny = alnx2 + blnx + cln

Solving for variable 'l'.

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

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

Reorder the terms:
-1alnx2 + lny = alnx2 + -1alnx2 + blnx + cln

Combine like terms: alnx2 + -1alnx2 = 0
-1alnx2 + lny = 0 + blnx + cln
-1alnx2 + lny = blnx + cln

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

Combine like terms: blnx + -1blnx = 0
-1alnx2 + -1blnx + lny = 0 + cln
-1alnx2 + -1blnx + lny = cln

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

Combine like terms: cln + -1cln = 0
-1alnx2 + -1blnx + -1cln + lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1ax2 + -1bx + -1c + 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 '(-1ax2 + -1bx + -1c + y)' equal to zero and attempt to solve: Simplifying -1ax2 + -1bx + -1c + y = 0 Solving -1ax2 + -1bx + -1c + y = 0 Move all terms containing l to the left, all other terms to the right. Add 'ax2' to each side of the equation. -1ax2 + -1bx + -1c + ax2 + y = 0 + ax2 Reorder the terms: -1ax2 + ax2 + -1bx + -1c + y = 0 + ax2 Combine like terms: -1ax2 + ax2 = 0 0 + -1bx + -1c + y = 0 + ax2 -1bx + -1c + y = 0 + ax2 Remove the zero: -1bx + -1c + y = ax2 Add 'bx' to each side of the equation. -1bx + -1c + bx + y = ax2 + bx Reorder the terms: -1bx + bx + -1c + y = ax2 + bx Combine like terms: -1bx + bx = 0 0 + -1c + y = ax2 + bx -1c + y = ax2 + bx Add 'c' to each side of the equation. -1c + c + y = ax2 + bx + c Combine like terms: -1c + c = 0 0 + y = ax2 + bx + c y = ax2 + bx + c Add '-1y' to each side of the equation. y + -1y = ax2 + bx + c + -1y Combine like terms: y + -1y = 0 0 = ax2 + bx + c + -1y Simplifying 0 = ax2 + bx + c + -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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