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

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


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

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

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

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

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

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

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

Solving
-1glo + glox = -4glo

Solving for variable 'g'.

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

Add '4glo' to each side of the equation.
-1glo + 4glo + glox = -4glo + 4glo

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

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

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(3 + x) = 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x 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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