Log(7x+1)=2log(x+3)-log^2

Solution for Log(7x+1)=2log(x+3)-log^2 equation:

Simplifying
Log(7x + 1) = 2log(x + 3) + -1log2

Reorder the terms:
goL(1 + 7x) = 2log(x + 3) + -1log2
(1 * goL + 7x * goL) = 2log(x + 3) + -1log2
(1goL + 7goxL) = 2log(x + 3) + -1log2

Reorder the terms:
1goL + 7goxL = 2glo(3 + x) + -1log2
1goL + 7goxL = (3 * 2glo + x * 2glo) + -1log2
1goL + 7goxL = (6glo + 2glox) + -1log2

Solving
1goL + 7goxL = 6glo + 2glox + -1g2lo

Solving for variable 'g'.

Reorder the terms:
-6glo + -2glox + 1goL + 7goxL + g2lo = 6glo + 2glox + -1g2lo + -6glo + -2glox + g2lo

Reorder the terms:
-6glo + -2glox + 1goL + 7goxL + g2lo = 6glo + -6glo + 2glox + -2glox + -1g2lo + g2lo

Combine like terms: 6glo + -6glo = 0
-6glo + -2glox + 1goL + 7goxL + g2lo = 0 + 2glox + -2glox + -1g2lo + g2lo
-6glo + -2glox + 1goL + 7goxL + g2lo = 2glox + -2glox + -1g2lo + g2lo

Combine like terms: 2glox + -2glox = 0
-6glo + -2glox + 1goL + 7goxL + g2lo = 0 + -1g2lo + g2lo
-6glo + -2glox + 1goL + 7goxL + g2lo = -1g2lo + g2lo

Combine like terms: -1g2lo + g2lo = 0
-6glo + -2glox + 1goL + 7goxL + g2lo = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(-6l + -2lx + L + 7xL + gl) = 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 '(-6l + -2lx + L + 7xL + gl)' equal to zero and attempt to solve:

Simplifying
-6l + -2lx + L + 7xL + gl = 0

Reorder the terms:
L + gl + -6l + -2lx + 7xL = 0

Solving
L + gl + -6l + -2lx + 7xL = 0

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

Add '-1L' to each side of the equation.
L + gl + -6l + -2lx + -1L + 7xL = 0 + -1L

Reorder the terms:
L + -1L + gl + -6l + -2lx + 7xL = 0 + -1L

Combine like terms: L + -1L = 0
0 + gl + -6l + -2lx + 7xL = 0 + -1L
gl + -6l + -2lx + 7xL = 0 + -1L
Remove the zero:
gl + -6l + -2lx + 7xL = -1L

Add '6l' to each side of the equation.
gl + -6l + -2lx + 6l + 7xL = -1L + 6l

Reorder the terms:
gl + -6l + 6l + -2lx + 7xL = -1L + 6l

Combine like terms: -6l + 6l = 0
gl + 0 + -2lx + 7xL = -1L + 6l
gl + -2lx + 7xL = -1L + 6l

Add '2lx' to each side of the equation.
gl + -2lx + 2lx + 7xL = -1L + 6l + 2lx

Combine like terms: -2lx + 2lx = 0
gl + 0 + 7xL = -1L + 6l + 2lx
gl + 7xL = -1L + 6l + 2lx

Add '-7xL' to each side of the equation.
gl + 7xL + -7xL = -1L + 6l + 2lx + -7xL

Combine like terms: 7xL + -7xL = 0
gl + 0 = -1L + 6l + 2lx + -7xL
gl = -1L + 6l + 2lx + -7xL

Divide each side by 'l'.
g = -1l-1L + 6 + 2x + -7l-1xL

Simplifying
g = -1l-1L + 6 + 2x + -7l-1xL

Reorder the terms:
g = 6 + -1l-1L + -7l-1xL + 2x
Solution
g = {6 + -1l-1L + -7l-1xL + 2x}