log(x+2)+log(x-1)=log(13-2x)

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Solution for log(x+2)+log(x-1)=log(13-2x) equation:


Simplifying
log(x + 2) + log(x + -1) = log(13 + -2x)

Reorder the terms:
glo(2 + x) + log(x + -1) = log(13 + -2x)
(2 * glo + x * glo) + log(x + -1) = log(13 + -2x)
(2glo + glox) + log(x + -1) = log(13 + -2x)

Reorder the terms:
2glo + glox + glo(-1 + x) = log(13 + -2x)
2glo + glox + (-1 * glo + x * glo) = log(13 + -2x)
2glo + glox + (-1glo + glox) = log(13 + -2x)

Reorder the terms:
2glo + -1glo + glox + glox = log(13 + -2x)

Combine like terms: 2glo + -1glo = 1glo
1glo + glox + glox = log(13 + -2x)

Combine like terms: glox + glox = 2glox
1glo + 2glox = log(13 + -2x)
1glo + 2glox = (13 * glo + -2x * glo)
1glo + 2glox = (13glo + -2glox)

Solving
1glo + 2glox = 13glo + -2glox

Solving for variable 'g'.

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

Add '-13glo' to each side of the equation.
1glo + -13glo + 2glox = 13glo + -13glo + -2glox

Combine like terms: 1glo + -13glo = -12glo
-12glo + 2glox = 13glo + -13glo + -2glox

Combine like terms: 13glo + -13glo = 0
-12glo + 2glox = 0 + -2glox
-12glo + 2glox = -2glox

Add '2glox' to each side of the equation.
-12glo + 2glox + 2glox = -2glox + 2glox

Combine like terms: 2glox + 2glox = 4glox
-12glo + 4glox = -2glox + 2glox

Combine like terms: -2glox + 2glox = 0
-12glo + 4glox = 0

Factor out the Greatest Common Factor (GCF), '4glo'.
4glo(-3 + x) = 0

Ignore the factor 4.

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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