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

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


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

Remove parenthesis around (3x)
glo * 3x + log(x + -2) = log(x + -4)

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

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

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

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

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

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

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

Solving for variable 'g'.

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

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

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

Combine like terms: -4glo + 4glo = 0
2glo + 4glox = 0 + glox
2glo + 4glox = glox

Add '-1glox' to each side of the equation.
2glo + 4glox + -1glox = glox + -1glox

Combine like terms: 4glox + -1glox = 3glox
2glo + 3glox = glox + -1glox

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

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