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

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

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

Reorder the terms:
goL(-4 + x) + log(x + -2) = log(x + 3) + log(x + -4)
(-4 * goL + x * goL) + log(x + -2) = log(x + 3) + log(x + -4)
(-4goL + goxL) + log(x + -2) = log(x + 3) + log(x + -4)

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

Reorder the terms:
-2glo + glox + -4goL + goxL = log(x + 3) + log(x + -4)

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

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

Reorder the terms:
-2glo + glox + -4goL + goxL = 3glo + -4glo + glox + glox

Combine like terms: 3glo + -4glo = -1glo
-2glo + glox + -4goL + goxL = -1glo + glox + glox

Combine like terms: glox + glox = 2glox
-2glo + glox + -4goL + goxL = -1glo + 2glox

Solving
-2glo + glox + -4goL + goxL = -1glo + 2glox

Solving for variable 'g'.

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

Add 'glo' to each side of the equation.
-2glo + glox + -4goL + glo + goxL = -1glo + glo + 2glox

Reorder the terms:
-2glo + glo + glox + -4goL + goxL = -1glo + glo + 2glox

Combine like terms: -2glo + glo = -1glo
-1glo + glox + -4goL + goxL = -1glo + glo + 2glox

Combine like terms: -1glo + glo = 0
-1glo + glox + -4goL + goxL = 0 + 2glox
-1glo + glox + -4goL + goxL = 2glox

Add '-2glox' to each side of the equation.
-1glo + glox + -4goL + -2glox + goxL = 2glox + -2glox

Reorder the terms:
-1glo + glox + -2glox + -4goL + goxL = 2glox + -2glox

Combine like terms: glox + -2glox = -1glox
-1glo + -1glox + -4goL + goxL = 2glox + -2glox

Combine like terms: 2glox + -2glox = 0
-1glo + -1glox + -4goL + goxL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(-1l + -1lx + -4L + xL) = 0

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 '(-1l + -1lx + -4L + xL)' equal to zero and attempt to solve:

Simplifying
-1l + -1lx + -4L + xL = 0

Reorder the terms:
-4L + -1l + -1lx + xL = 0

Solving
-4L + -1l + -1lx + xL = 0

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

Add '4L' to each side of the equation.
-4L + -1l + -1lx + 4L + xL = 0 + 4L

Reorder the terms:
-4L + 4L + -1l + -1lx + xL = 0 + 4L

Combine like terms: -4L + 4L = 0
0 + -1l + -1lx + xL = 0 + 4L
-1l + -1lx + xL = 0 + 4L
Remove the zero:
-1l + -1lx + xL = 4L

Add 'l' to each side of the equation.
-1l + -1lx + l + xL = 4L + l

Reorder the terms:
-1l + l + -1lx + xL = 4L + l

Combine like terms: -1l + l = 0
0 + -1lx + xL = 4L + l
-1lx + xL = 4L + l

Add 'lx' to each side of the equation.
-1lx + lx + xL = 4L + l + lx

Combine like terms: -1lx + lx = 0
0 + xL = 4L + l + lx
xL = 4L + l + lx

Add '-1xL' to each side of the equation.
xL + -1xL = 4L + l + lx + -1xL

Combine like terms: xL + -1xL = 0
0 = 4L + l + lx + -1xL

Simplifying
0 = 4L + l + 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.