Log(6)(4-2x)=log(6)(10-x)

Solution for Log(6)(4-2x)=log(6)(10-x) equation:

Simplifying
Log(6)(4 + -2x) = log(6)(10 + -1x)

Reorder the terms for easier multiplication:
6goL(4 + -2x) = log(6)(10 + -1x)
(4 * 6goL + -2x * 6goL) = log(6)(10 + -1x)
(24goL + -12goxL) = log(6)(10 + -1x)

Reorder the terms for easier multiplication:
24goL + -12goxL = 6glo(10 + -1x)
24goL + -12goxL = (10 * 6glo + -1x * 6glo)
24goL + -12goxL = (60glo + -6glox)

Solving
24goL + -12goxL = 60glo + -6glox

Solving for variable 'g'.

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

Add '-60glo' to each side of the equation.
24goL + -60glo + -12goxL = 60glo + -60glo + -6glox

Reorder the terms:
-60glo + 24goL + -12goxL = 60glo + -60glo + -6glox

Combine like terms: 60glo + -60glo = 0
-60glo + 24goL + -12goxL = 0 + -6glox
-60glo + 24goL + -12goxL = -6glox

Add '6glox' to each side of the equation.
-60glo + 24goL + 6glox + -12goxL = -6glox + 6glox

Reorder the terms:
-60glo + 6glox + 24goL + -12goxL = -6glox + 6glox

Combine like terms: -6glox + 6glox = 0
-60glo + 6glox + 24goL + -12goxL = 0

Factor out the Greatest Common Factor (GCF), '6go'.
6go(-10l + lx + 4L + -2xL) = 0

Ignore the factor 6.
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 '(-10l + lx + 4L + -2xL)' equal to zero and attempt to solve:

Simplifying
-10l + lx + 4L + -2xL = 0

Reorder the terms:
4L + -10l + lx + -2xL = 0

Solving
4L + -10l + lx + -2xL = 0

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

Add '-4L' to each side of the equation.
4L + -10l + lx + -4L + -2xL = 0 + -4L

Reorder the terms:
4L + -4L + -10l + lx + -2xL = 0 + -4L

Combine like terms: 4L + -4L = 0
0 + -10l + lx + -2xL = 0 + -4L
-10l + lx + -2xL = 0 + -4L
Remove the zero:
-10l + lx + -2xL = -4L

Add '10l' to each side of the equation.
-10l + lx + 10l + -2xL = -4L + 10l

Reorder the terms:
-10l + 10l + lx + -2xL = -4L + 10l

Combine like terms: -10l + 10l = 0
0 + lx + -2xL = -4L + 10l
lx + -2xL = -4L + 10l

Add '-1lx' to each side of the equation.
lx + -1lx + -2xL = -4L + 10l + -1lx

Combine like terms: lx + -1lx = 0
0 + -2xL = -4L + 10l + -1lx
-2xL = -4L + 10l + -1lx

Add '2xL' to each side of the equation.
-2xL + 2xL = -4L + 10l + -1lx + 2xL

Combine like terms: -2xL + 2xL = 0
0 = -4L + 10l + -1lx + 2xL

Simplifying
0 = -4L + 10l + -1lx + 2xL

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.