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

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


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

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

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

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

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

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

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

Solving
3glox = 2glo + glox

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

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

Add '-1glox' to each side of the equation.
-2glo + 3glox + -1glox = glox + -1glox

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

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

Factor out the Greatest Common Factor (GCF), '2glo'.
2glo(-1 + x) = 0

Ignore the factor 2.

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