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

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


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

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

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

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

Solving for variable 'g'.

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

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

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

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

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

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

Combine like terms: glox + -1glox = 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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