log(3x+1)-log(x-2)-2=0

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Solution for log(3x+1)-log(x-2)-2=0 equation:


Simplifying
log(3x + 1) + -1log(x + -2) + -2 = 0

Reorder the terms:
glo(1 + 3x) + -1log(x + -2) + -2 = 0
(1 * glo + 3x * glo) + -1log(x + -2) + -2 = 0
(1glo + 3glox) + -1log(x + -2) + -2 = 0

Reorder the terms:
1glo + 3glox + -1glo(-2 + x) + -2 = 0
1glo + 3glox + (-2 * -1glo + x * -1glo) + -2 = 0
1glo + 3glox + (2glo + -1glox) + -2 = 0

Reorder the terms:
-2 + 1glo + 2glo + 3glox + -1glox = 0

Combine like terms: 1glo + 2glo = 3glo
-2 + 3glo + 3glox + -1glox = 0

Combine like terms: 3glox + -1glox = 2glox
-2 + 3glo + 2glox = 0

Solving
-2 + 3glo + 2glox = 0

Solving for variable 'g'.

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

Add '2' to each side of the equation.
-2 + 3glo + 2 + 2glox = 0 + 2

Reorder the terms:
-2 + 2 + 3glo + 2glox = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3glo + 2glox = 0 + 2
3glo + 2glox = 0 + 2

Combine like terms: 0 + 2 = 2
3glo + 2glox = 2

Reorder the terms:
-2 + 3glo + 2glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 3glo + 2glox = 0

The solution to this equation could not be determined.

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