x=ln(4x^2-16x)

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


Simplifying
x = ln(4x2 + -16x)

Reorder the terms:
x = ln(-16x + 4x2)
x = (-16x * ln + 4x2 * ln)
x = (-16lnx + 4lnx2)

Solving
x = -16lnx + 4lnx2

Solving for variable 'x'.

Reorder the terms:
16lnx + -4lnx2 + x = -16lnx + 4lnx2 + 16lnx + -4lnx2

Reorder the terms:
16lnx + -4lnx2 + x = -16lnx + 16lnx + 4lnx2 + -4lnx2

Combine like terms: -16lnx + 16lnx = 0
16lnx + -4lnx2 + x = 0 + 4lnx2 + -4lnx2
16lnx + -4lnx2 + x = 4lnx2 + -4lnx2

Combine like terms: 4lnx2 + -4lnx2 = 0
16lnx + -4lnx2 + x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(16ln + -4lnx + 1) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(16ln + -4lnx + 1)' equal to zero and attempt to solve:

Simplifying
16ln + -4lnx + 1 = 0

Reorder the terms:
1 + 16ln + -4lnx = 0

Solving
1 + 16ln + -4lnx = 0

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

Add '-1' to each side of the equation.
1 + 16ln + -1 + -4lnx = 0 + -1

Reorder the terms:
1 + -1 + 16ln + -4lnx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 16ln + -4lnx = 0 + -1
16ln + -4lnx = 0 + -1

Combine like terms: 0 + -1 = -1
16ln + -4lnx = -1

Add '-16ln' to each side of the equation.
16ln + -16ln + -4lnx = -1 + -16ln

Combine like terms: 16ln + -16ln = 0
0 + -4lnx = -1 + -16ln
-4lnx = -1 + -16ln

Divide each side by '-4ln'.
x = 0.25l-1n-1 + 4

Simplifying
x = 0.25l-1n-1 + 4

Reorder the terms:
x = 4 + 0.25l-1n-1
Solution
x = {0, 4 + 0.25l-1n-1}

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