ln(y)=3ln((x^2)+4)+ln(32)-3ln(4)

Solution for ln(y)=3ln((x^2)+4)+ln(32)-3ln(4) equation:

Simplifying
ln(y) = 3ln((x2) + 4) + ln(32) + -3ln(4)

Multiply ln * y
lny = 3ln((x2) + 4) + ln(32) + -3ln(4)
lny = 3ln(x2 + 4) + ln(32) + -3ln(4)

Reorder the terms:
lny = 3ln(4 + x2) + ln(32) + -3ln(4)
lny = (4 * 3ln + x2 * 3ln) + ln(32) + -3ln(4)
lny = (12ln + 3lnx2) + ln(32) + -3ln(4)

Reorder the terms for easier multiplication:
lny = 12ln + 3lnx2 + 32ln + -3ln(4)

Reorder the terms for easier multiplication:
lny = 12ln + 3lnx2 + 32ln + -3 * 4ln

Multiply -3 * 4
lny = 12ln + 3lnx2 + 32ln + -12ln

Reorder the terms:
lny = 12ln + 32ln + -12ln + 3lnx2

Combine like terms: 12ln + 32ln = 44ln
lny = 44ln + -12ln + 3lnx2

Combine like terms: 44ln + -12ln = 32ln
lny = 32ln + 3lnx2

Solving
lny = 32ln + 3lnx2

Solving for variable 'l'.

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

Add '-32ln' to each side of the equation.
-32ln + lny = 32ln + -32ln + 3lnx2

Combine like terms: 32ln + -32ln = 0
-32ln + lny = 0 + 3lnx2
-32ln + lny = 3lnx2

Add '-3lnx2' to each side of the equation.
-32ln + -3lnx2 + lny = 3lnx2 + -3lnx2

Combine like terms: 3lnx2 + -3lnx2 = 0
-32ln + -3lnx2 + lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-32 + -3x2 + 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 '(-32 + -3x2 + y)' equal to zero and attempt to solve:

Simplifying
-32 + -3x2 + y = 0

Solving
-32 + -3x2 + y = 0

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

Add '32' to each side of the equation.
-32 + -3x2 + 32 + y = 0 + 32

Reorder the terms:
-32 + 32 + -3x2 + y = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -3x2 + y = 0 + 32
-3x2 + y = 0 + 32

Combine like terms: 0 + 32 = 32
-3x2 + y = 32

Add '3x2' to each side of the equation.
-3x2 + 3x2 + y = 32 + 3x2

Combine like terms: -3x2 + 3x2 = 0
0 + y = 32 + 3x2
y = 32 + 3x2

Add '-1y' to each side of the equation.
y + -1y = 32 + 3x2 + -1y

Combine like terms: y + -1y = 0
0 = 32 + 3x2 + -1y

Simplifying
0 = 32 + 3x2 + -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.