Ln(-3x)=ln(x^2+4)

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


Simplifying
Ln(-3x) = ln(x2 + 4)

Remove parenthesis around (-3x)
nL * -3x = ln(x2 + 4)

Reorder the terms for easier multiplication:
-3nL * x = ln(x2 + 4)

Multiply nL * x
-3nxL = ln(x2 + 4)

Reorder the terms:
-3nxL = ln(4 + x2)
-3nxL = (4 * ln + x2 * ln)
-3nxL = (4ln + lnx2)

Solving
-3nxL = 4ln + lnx2

Solving for variable 'n'.

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

Add '-4ln' to each side of the equation.
-4ln + -3nxL = 4ln + -4ln + lnx2

Combine like terms: 4ln + -4ln = 0
-4ln + -3nxL = 0 + lnx2
-4ln + -3nxL = lnx2

Add '-1lnx2' to each side of the equation.
-4ln + -1lnx2 + -3nxL = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
-4ln + -1lnx2 + -3nxL = 0

Factor out the Greatest Common Factor (GCF), '-1n'.
-1n(4l + lx2 + 3xL) = 0

Ignore the factor -1.

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(4l + lx2 + 3xL)' equal to zero and attempt to solve:

Simplifying
4l + lx2 + 3xL = 0

Solving
4l + lx2 + 3xL = 0

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

Add '-4l' to each side of the equation.
4l + lx2 + -4l + 3xL = 0 + -4l

Reorder the terms:
4l + -4l + lx2 + 3xL = 0 + -4l

Combine like terms: 4l + -4l = 0
0 + lx2 + 3xL = 0 + -4l
lx2 + 3xL = 0 + -4l
Remove the zero:
lx2 + 3xL = -4l

Add '-1lx2' to each side of the equation.
lx2 + -1lx2 + 3xL = -4l + -1lx2

Combine like terms: lx2 + -1lx2 = 0
0 + 3xL = -4l + -1lx2
3xL = -4l + -1lx2

Add '-3xL' to each side of the equation.
3xL + -3xL = -4l + -1lx2 + -3xL

Combine like terms: 3xL + -3xL = 0
0 = -4l + -1lx2 + -3xL

Simplifying
0 = -4l + -1lx2 + -3xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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