log(3x-2)+log(3x-1)=log(4x-3)2

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Solution for log(3x-2)+log(3x-1)=log(4x-3)2 equation:


Simplifying
log(3x + -2) + log(3x + -1) = log(4x + -3) * 2

Reorder the terms:
glo(-2 + 3x) + log(3x + -1) = log(4x + -3) * 2
(-2 * glo + 3x * glo) + log(3x + -1) = log(4x + -3) * 2
(-2glo + 3glox) + log(3x + -1) = log(4x + -3) * 2

Reorder the terms:
-2glo + 3glox + glo(-1 + 3x) = log(4x + -3) * 2
-2glo + 3glox + (-1 * glo + 3x * glo) = log(4x + -3) * 2
-2glo + 3glox + (-1glo + 3glox) = log(4x + -3) * 2

Reorder the terms:
-2glo + -1glo + 3glox + 3glox = log(4x + -3) * 2

Combine like terms: -2glo + -1glo = -3glo
-3glo + 3glox + 3glox = log(4x + -3) * 2

Combine like terms: 3glox + 3glox = 6glox
-3glo + 6glox = log(4x + -3) * 2

Reorder the terms:
-3glo + 6glox = glo(-3 + 4x) * 2

Reorder the terms for easier multiplication:
-3glo + 6glox = 2glo(-3 + 4x)
-3glo + 6glox = (-3 * 2glo + 4x * 2glo)
-3glo + 6glox = (-6glo + 8glox)

Solving
-3glo + 6glox = -6glo + 8glox

Solving for variable 'g'.

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

Add '6glo' to each side of the equation.
-3glo + 6glo + 6glox = -6glo + 6glo + 8glox

Combine like terms: -3glo + 6glo = 3glo
3glo + 6glox = -6glo + 6glo + 8glox

Combine like terms: -6glo + 6glo = 0
3glo + 6glox = 0 + 8glox
3glo + 6glox = 8glox

Add '-8glox' to each side of the equation.
3glo + 6glox + -8glox = 8glox + -8glox

Combine like terms: 6glox + -8glox = -2glox
3glo + -2glox = 8glox + -8glox

Combine like terms: 8glox + -8glox = 0
3glo + -2glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(3 + -2x) = 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 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Add '2x' to each side of the equation. -2x + 2x = -3 + 2x Combine like terms: -2x + 2x = 0 0 = -3 + 2x Simplifying 0 = -3 + 2x 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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