log(x)-log(x-1)=log(x-3)

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Solution for log(x)-log(x-1)=log(x-3) equation:


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

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

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

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

Combine like terms: glox + -1glox = 0
1glo + 0 = log(x + -3)
1glo = log(x + -3)

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

Solving
1glo = -3glo + glox

Solving for variable 'g'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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