log(6)3x+log(6)(x-1)=3

Solution for log(6)3x+log(6)(x-1)=3 equation:

Simplifying
log(6) * 3x + log(6)(x + -1) = 3

Reorder the terms for easier multiplication:
6 * 3glo * x + log(6)(x + -1) = 3

Multiply 6 * 3
18glo * x + log(6)(x + -1) = 3

Multiply glo * x
18glox + log(6)(x + -1) = 3

Reorder the terms:
18glox + glo * 6(-1 + x) = 3

Reorder the terms for easier multiplication:
18glox + 6glo(-1 + x) = 3
18glox + (-1 * 6glo + x * 6glo) = 3
18glox + (-6glo + 6glox) = 3

Reorder the terms:
-6glo + 18glox + 6glox = 3

Combine like terms: 18glox + 6glox = 24glox
-6glo + 24glox = 3

Solving
-6glo + 24glox = 3

Solving for variable 'g'.

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

Reorder the terms:
-3 + -6glo + 24glox = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -6glo + 24glox = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -2glo + 8glox) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -2glo + 8glox)' equal to zero and attempt to solve:

Simplifying
-1 + -2glo + 8glox = 0

Solving
-1 + -2glo + 8glox = 0

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

Add '1' to each side of the equation.
-1 + -2glo + 1 + 8glox = 0 + 1

Reorder the terms:
-1 + 1 + -2glo + 8glox = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2glo + 8glox = 0 + 1
-2glo + 8glox = 0 + 1

Combine like terms: 0 + 1 = 1
-2glo + 8glox = 1

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.