Log(9)(x+6)-log(9)x=log(9)2

Solution for Log(9)(x+6)-log(9)x=log(9)2 equation:

Simplifying
Log(9)(x + 6) + -1log(9) * x = log(9) * 2

Reorder the terms:
goL * 9(6 + x) + -1log(9) * x = log(9) * 2

Reorder the terms for easier multiplication:
9goL(6 + x) + -1log(9) * x = log(9) * 2
(6 * 9goL + x * 9goL) + -1log(9) * x = log(9) * 2
(54goL + 9goxL) + -1log(9) * x = log(9) * 2

Reorder the terms for easier multiplication:
54goL + 9goxL + -1 * 9glo * x = log(9) * 2

Multiply -1 * 9
54goL + 9goxL + -9glo * x = log(9) * 2

Multiply glo * x
54goL + 9goxL + -9glox = log(9) * 2

Reorder the terms:
-9glox + 54goL + 9goxL = log(9) * 2

Reorder the terms for easier multiplication:
-9glox + 54goL + 9goxL = 9 * 2glo

Multiply 9 * 2
-9glox + 54goL + 9goxL = 18glo

Solving
-9glox + 54goL + 9goxL = 18glo

Solving for variable 'g'.

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

Add '-18glo' to each side of the equation.
-9glox + 54goL + -18glo + 9goxL = 18glo + -18glo

Reorder the terms:
-18glo + -9glox + 54goL + 9goxL = 18glo + -18glo

Combine like terms: 18glo + -18glo = 0
-18glo + -9glox + 54goL + 9goxL = 0

Factor out the Greatest Common Factor (GCF), '9go'.
9go(-2l + -1lx + 6L + xL) = 0

Ignore the factor 9.
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 '(-2l + -1lx + 6L + xL)' equal to zero and attempt to solve:

Simplifying
-2l + -1lx + 6L + xL = 0

Reorder the terms:
6L + -2l + -1lx + xL = 0

Solving
6L + -2l + -1lx + xL = 0

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

Add '-6L' to each side of the equation.
6L + -2l + -1lx + -6L + xL = 0 + -6L

Reorder the terms:
6L + -6L + -2l + -1lx + xL = 0 + -6L

Combine like terms: 6L + -6L = 0
0 + -2l + -1lx + xL = 0 + -6L
-2l + -1lx + xL = 0 + -6L
Remove the zero:
-2l + -1lx + xL = -6L

Add '2l' to each side of the equation.
-2l + -1lx + 2l + xL = -6L + 2l

Reorder the terms:
-2l + 2l + -1lx + xL = -6L + 2l

Combine like terms: -2l + 2l = 0
0 + -1lx + xL = -6L + 2l
-1lx + xL = -6L + 2l

Add 'lx' to each side of the equation.
-1lx + lx + xL = -6L + 2l + lx

Combine like terms: -1lx + lx = 0
0 + xL = -6L + 2l + lx
xL = -6L + 2l + lx

Add '-1xL' to each side of the equation.
xL + -1xL = -6L + 2l + lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -6L + 2l + lx + -1xL

Simplifying
0 = -6L + 2l + 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.