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

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


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

Multiply glo * x
2glox = log(2) + log(3x + -4)

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

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

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

Solving
2glox = -2glo + 3glox

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.
2glo + 2glox = -2glo + 2glo + 3glox

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(2 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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