ln(16+2b)=ln(b^2-4b)

Solution for ln(16+2b)=ln(b^2-4b) equation:

Simplifying
ln(16 + 2b) = ln(b2 + -4b)
(16 * ln + 2b * ln) = ln(b2 + -4b)

Reorder the terms:
(2bln + 16ln) = ln(b2 + -4b)
(2bln + 16ln) = ln(b2 + -4b)

Reorder the terms:
2bln + 16ln = ln(-4b + b2)
2bln + 16ln = (-4b * ln + b2 * ln)
2bln + 16ln = (-4bln + b2ln)

Solving
2bln + 16ln = -4bln + b2ln

Solving for variable 'b'.

Reorder the terms:
2bln + 4bln + -1b2ln + 16ln = -4bln + b2ln + 4bln + -1b2ln

Combine like terms: 2bln + 4bln = 6bln
6bln + -1b2ln + 16ln = -4bln + b2ln + 4bln + -1b2ln

Reorder the terms:
6bln + -1b2ln + 16ln = -4bln + 4bln + b2ln + -1b2ln

Combine like terms: -4bln + 4bln = 0
6bln + -1b2ln + 16ln = 0 + b2ln + -1b2ln
6bln + -1b2ln + 16ln = b2ln + -1b2ln

Combine like terms: b2ln + -1b2ln = 0
6bln + -1b2ln + 16ln = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(6b + -1b2 + 16) = 0

Factor a trinomial.
ln((-1b + -2)(b + -8)) = 0

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

Simplifying
ln = 0

Solving
ln = 0

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

Add '-1ln' to each side of the equation.
ln + -1ln = 0 + -1ln
Remove the zero:
0 = -1ln

Simplifying
0 = -1ln

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 '(-1b + -2)' equal to zero and attempt to solve:

Simplifying
-1b + -2 = 0

Reorder the terms:
-2 + -1b = 0

Solving
-2 + -1b = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1b = 0 + 2
-1b = 0 + 2

Combine like terms: 0 + 2 = 2
-1b = 2

Divide each side by '-1'.
b = -2

Simplifying
b = -2
Subproblem 3
Set the factor '(b + -8)' equal to zero and attempt to solve:

Simplifying
b + -8 = 0

Reorder the terms:
-8 + b = 0

Solving
-8 + b = 0

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

Add '8' to each side of the equation.
-8 + 8 + b = 0 + 8

Combine like terms: -8 + 8 = 0
0 + b = 0 + 8
b = 0 + 8

Combine like terms: 0 + 8 = 8
b = 8

Simplifying
b = 8
Solution
b = {-2, 8}