Log(3)(x+8)-log(3)(x-6)=3log(3)2

Solution for Log(3)(x+8)-log(3)(x-6)=3log(3)2 equation:

Simplifying
Log(3)(x + 8) + -1log(3)(x + -6) = 3log(3) * 2

Reorder the terms:
goL * 3(8 + x) + -1log(3)(x + -6) = 3log(3) * 2

Reorder the terms for easier multiplication:
3goL(8 + x) + -1log(3)(x + -6) = 3log(3) * 2
(8 * 3goL + x * 3goL) + -1log(3)(x + -6) = 3log(3) * 2
(24goL + 3goxL) + -1log(3)(x + -6) = 3log(3) * 2

Reorder the terms:
24goL + 3goxL + -1glo * 3(-6 + x) = 3log(3) * 2

Reorder the terms for easier multiplication:
24goL + 3goxL + -1 * 3glo(-6 + x) = 3log(3) * 2

Multiply -1 * 3
24goL + 3goxL + -3glo(-6 + x) = 3log(3) * 2
24goL + 3goxL + (-6 * -3glo + x * -3glo) = 3log(3) * 2
24goL + 3goxL + (18glo + -3glox) = 3log(3) * 2

Reorder the terms:
18glo + -3glox + 24goL + 3goxL = 3log(3) * 2

Reorder the terms for easier multiplication:
18glo + -3glox + 24goL + 3goxL = 3 * 3 * 2glo

Multiply 3 * 3
18glo + -3glox + 24goL + 3goxL = 9 * 2glo

Multiply 9 * 2
18glo + -3glox + 24goL + 3goxL = 18glo

Add '-18glo' to each side of the equation.
18glo + -3glox + 24goL + -18glo + 3goxL = 18glo + -18glo

Reorder the terms:
18glo + -18glo + -3glox + 24goL + 3goxL = 18glo + -18glo

Combine like terms: 18glo + -18glo = 0
0 + -3glox + 24goL + 3goxL = 18glo + -18glo
-3glox + 24goL + 3goxL = 18glo + -18glo

Combine like terms: 18glo + -18glo = 0
-3glox + 24goL + 3goxL = 0

Solving
-3glox + 24goL + 3goxL = 0

Solving for variable 'g'.

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

Factor out the Greatest Common Factor (GCF), '3go'.
3go(-1lx + 8L + xL) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'go' equal to zero and attempt to solve:

Simplifying
go = 0

Solving
go = 0

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

Simplifying
go = 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 '(-1lx + 8L + xL)' equal to zero and attempt to solve:

Simplifying
-1lx + 8L + xL = 0

Reorder the terms:
8L + -1lx + xL = 0

Solving
8L + -1lx + xL = 0

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

Add '-8L' to each side of the equation.
8L + -1lx + -8L + xL = 0 + -8L

Reorder the terms:
8L + -8L + -1lx + xL = 0 + -8L

Combine like terms: 8L + -8L = 0
0 + -1lx + xL = 0 + -8L
-1lx + xL = 0 + -8L
Remove the zero:
-1lx + xL = -8L

Add 'lx' to each side of the equation.
-1lx + lx + xL = -8L + lx

Combine like terms: -1lx + lx = 0
0 + xL = -8L + lx
xL = -8L + lx

Add '-1xL' to each side of the equation.
xL + -1xL = -8L + lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -8L + lx + -1xL

Simplifying
0 = -8L + lx + -1xL

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.