(.5)ln(x^2+1)-4ln(.5)-(.5)[ln(x-4)+lnx]=0

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Solution for (.5)ln(x^2+1)-4ln(.5)-(.5)[ln(x-4)+lnx]=0 equation: 


Simplifying
(0.5) * ln(x2 + 1) + -4ln(0.5) + -1(0.5)[ln(x + -4) + lnx] = 0

Reorder the terms:
0.5ln(1 + x2) + -4ln(0.5) + -1(0.5)[ln(x + -4) + lnx] = 0
(1 * 0.5ln + x2 * 0.5ln) + -4ln(0.5) + -1(0.5)[ln(x + -4) + lnx] = 0
(0.5ln + 0.5lnx2) + -4ln(0.5) + -1(0.5)[ln(x + -4) + lnx] = 0

Reorder the terms for easier multiplication:
0.5ln + 0.5lnx2 + -4 * 0.5ln + -1(0.5)[ln(x + -4) + lnx] = 0

Multiply -4 * 0.5
0.5ln + 0.5lnx2 + -2ln + -1(0.5)[ln(x + -4) + lnx] = 0

Reorder the terms:
0.5ln + 0.5lnx2 + -2ln + -1 * 0.5[ln(-4 + x) + lnx] = 0
0.5ln + 0.5lnx2 + -2ln + -1 * 0.5[(-4 * ln + x * ln) + lnx] = 0
0.5ln + 0.5lnx2 + -2ln + -1 * 0.5[(-4ln + lnx) + lnx] = 0

Combine like terms: lnx + lnx = 2lnx
0.5ln + 0.5lnx2 + -2ln + -1 * 0.5[-4ln + 2lnx] = 0

Multiply -1 * 0.5
0.5ln + 0.5lnx2 + -2ln + -0.5[-4ln + 2lnx] = 0
0.5ln + 0.5lnx2 + -2ln + [-4ln * -0.5 + 2lnx * -0.5] = 0
0.5ln + 0.5lnx2 + -2ln + [2ln + -1lnx] = 0

Reorder the terms:
0.5ln + -2ln + 2ln + -1lnx + 0.5lnx2 = 0

Combine like terms: 0.5ln + -2ln = -1.5ln
-1.5ln + 2ln + -1lnx + 0.5lnx2 = 0

Combine like terms: -1.5ln + 2ln = 0.5ln
0.5ln + -1lnx + 0.5lnx2 = 0

Solving
0.5ln + -1lnx + 0.5lnx2 = 0

Solving for variable 'l'.

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

The solution to this equation could not be determined.

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