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

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


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

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

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

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

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

Combine like terms: 2glox + glox = 3glox
1glo + 3glox = 2log(x + 1)

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

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

Solving for variable 'g'.

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

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

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

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

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

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

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

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