log(3x-4)=log(x-6)

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Solution for log(3x-4)=log(x-6) equation:


Simplifying
log(3x + -4) = log(x + -6)

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

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

Solving
-4glo + 3glox = -6glo + glox

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.
-4glo + 6glo + 3glox = -6glo + 6glo + glox

Combine like terms: -4glo + 6glo = 2glo
2glo + 3glox = -6glo + 6glo + glox

Combine like terms: -6glo + 6glo = 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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