log(x-2)-log(x^2)=-log(3x)

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Solution for log(x-2)-log(x^2)=-log(3x) equation:


Simplifying
log(x + -2) + -1log(x2) = -1log(3x)

Reorder the terms:
glo(-2 + x) + -1log(x2) = -1log(3x)
(-2 * glo + x * glo) + -1log(x2) = -1log(3x)
(-2glo + glox) + -1log(x2) = -1log(3x)

Multiply glo * x2
-2glo + glox + -1glox2 = -1log(3x)

Remove parenthesis around (3x)
-2glo + glox + -1glox2 = -1glo * 3x

Reorder the terms for easier multiplication:
-2glo + glox + -1glox2 = -1 * 3glo * x

Multiply -1 * 3
-2glo + glox + -1glox2 = -3glo * x

Multiply glo * x
-2glo + glox + -1glox2 = -3glox

Solving
-2glo + glox + -1glox2 = -3glox

Solving for variable 'g'.

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

Add '3glox' to each side of the equation.
-2glo + glox + 3glox + -1glox2 = -3glox + 3glox

Combine like terms: glox + 3glox = 4glox
-2glo + 4glox + -1glox2 = -3glox + 3glox

Combine like terms: -3glox + 3glox = 0
-2glo + 4glox + -1glox2 = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-2 + 4x + -1x2) = 0

Subproblem 1

Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 4x + -1x2 = 0 Solving -2 + 4x + -1x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 4x + 2 + -1x2 = 0 + 2 Reorder the terms: -2 + 2 + 4x + -1x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4x + -1x2 = 0 + 2 4x + -1x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4x + -1x2 = 2 Add '-4x' to each side of the equation. 4x + -4x + -1x2 = 2 + -4x Combine like terms: 4x + -4x = 0 0 + -1x2 = 2 + -4x -1x2 = 2 + -4x Add 'x2' to each side of the equation. -1x2 + x2 = 2 + -4x + x2 Combine like terms: -1x2 + x2 = 0 0 = 2 + -4x + x2 Simplifying 0 = 2 + -4x + x2 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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