log(x-1)+log(x-3)=log(3x-7)

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Solution for log(x-1)+log(x-3)=log(3x-7) equation:


Simplifying
log(x + -1) + log(x + -3) = log(3x + -7)

Reorder the terms:
glo(-1 + x) + log(x + -3) = log(3x + -7)
(-1 * glo + x * glo) + log(x + -3) = log(3x + -7)
(-1glo + glox) + log(x + -3) = log(3x + -7)

Reorder the terms:
-1glo + glox + glo(-3 + x) = log(3x + -7)
-1glo + glox + (-3 * glo + x * glo) = log(3x + -7)
-1glo + glox + (-3glo + glox) = log(3x + -7)

Reorder the terms:
-1glo + -3glo + glox + glox = log(3x + -7)

Combine like terms: -1glo + -3glo = -4glo
-4glo + glox + glox = log(3x + -7)

Combine like terms: glox + glox = 2glox
-4glo + 2glox = log(3x + -7)

Reorder the terms:
-4glo + 2glox = glo(-7 + 3x)
-4glo + 2glox = (-7 * glo + 3x * glo)
-4glo + 2glox = (-7glo + 3glox)

Solving
-4glo + 2glox = -7glo + 3glox

Solving for variable 'g'.

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

Add '7glo' to each side of the equation.
-4glo + 7glo + 2glox = -7glo + 7glo + 3glox

Combine like terms: -4glo + 7glo = 3glo
3glo + 2glox = -7glo + 7glo + 3glox

Combine like terms: -7glo + 7glo = 0
3glo + 2glox = 0 + 3glox
3glo + 2glox = 3glox

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

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

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

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