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

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


Simplifying
ln(x) + ln(x + -2) = ln(x((x2) + 4))

Multiply ln * x
lnx + ln(x + -2) = ln(x((x2) + 4))

Reorder the terms:
lnx + ln(-2 + x) = ln(x((x2) + 4))
lnx + (-2 * ln + x * ln) = ln(x((x2) + 4))
lnx + (-2ln + lnx) = ln(x((x2) + 4))

Reorder the terms:
-2ln + lnx + lnx = ln(x((x2) + 4))

Combine like terms: lnx + lnx = 2lnx
-2ln + 2lnx = ln(x((x2) + 4))
-2ln + 2lnx = ln(x(x2 + 4))

Reorder the terms:
-2ln + 2lnx = ln(x(4 + x2))
-2ln + 2lnx = ln((4 * x + x2 * x))
-2ln + 2lnx = ln((4x + x3))
-2ln + 2lnx = (4x * ln + x3 * ln)
-2ln + 2lnx = (4lnx + lnx3)

Solving
-2ln + 2lnx = 4lnx + lnx3

Solving for variable 'l'.

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

Add '-4lnx' to each side of the equation.
-2ln + 2lnx + -4lnx = 4lnx + -4lnx + lnx3

Combine like terms: 2lnx + -4lnx = -2lnx
-2ln + -2lnx = 4lnx + -4lnx + lnx3

Combine like terms: 4lnx + -4lnx = 0
-2ln + -2lnx = 0 + lnx3
-2ln + -2lnx = lnx3

Add '-1lnx3' to each side of the equation.
-2ln + -2lnx + -1lnx3 = lnx3 + -1lnx3

Combine like terms: lnx3 + -1lnx3 = 0
-2ln + -2lnx + -1lnx3 = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(2 + 2x + x3) = 0

Ignore the factor -1.

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 '(2 + 2x + x3)' equal to zero and attempt to solve:

Simplifying
2 + 2x + x3 = 0

Solving
2 + 2x + x3 = 0

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

Add '-2' to each side of the equation.
2 + 2x + -2 + x3 = 0 + -2

Reorder the terms:
2 + -2 + 2x + x3 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2x + x3 = 0 + -2
2x + x3 = 0 + -2

Combine like terms: 0 + -2 = -2
2x + x3 = -2

Add '-2x' to each side of the equation.
2x + -2x + x3 = -2 + -2x

Combine like terms: 2x + -2x = 0
0 + x3 = -2 + -2x
x3 = -2 + -2x

Add '-1x3' to each side of the equation.
x3 + -1x3 = -2 + -2x + -1x3

Combine like terms: x3 + -1x3 = 0
0 = -2 + -2x + -1x3

Simplifying
0 = -2 + -2x + -1x3

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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