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

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


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

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

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

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

Combine like terms: 6glo + -1glo = 5glo
1goL + 7goxL = 5glo + 2glox

Solving
1goL + 7goxL = 5glo + 2glox

Solving for variable 'g'.

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

Add '-5glo' to each side of the equation.
1goL + -5glo + 7goxL = 5glo + -5glo + 2glox

Reorder the terms:
-5glo + 1goL + 7goxL = 5glo + -5glo + 2glox

Combine like terms: 5glo + -5glo = 0
-5glo + 1goL + 7goxL = 0 + 2glox
-5glo + 1goL + 7goxL = 2glox

Add '-2glox' to each side of the equation.
-5glo + 1goL + -2glox + 7goxL = 2glox + -2glox

Reorder the terms:
-5glo + -2glox + 1goL + 7goxL = 2glox + -2glox

Combine like terms: 2glox + -2glox = 0
-5glo + -2glox + 1goL + 7goxL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(-5l + -2lx + L + 7xL) = 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 '(-5l + -2lx + L + 7xL)' equal to zero and attempt to solve: Simplifying -5l + -2lx + L + 7xL = 0 Reorder the terms: L + -5l + -2lx + 7xL = 0 Solving L + -5l + -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 + -5l + -2lx + -1L + 7xL = 0 + -1L Reorder the terms: L + -1L + -5l + -2lx + 7xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -5l + -2lx + 7xL = 0 + -1L -5l + -2lx + 7xL = 0 + -1L Remove the zero: -5l + -2lx + 7xL = -1L Add '5l' to each side of the equation. -5l + -2lx + 5l + 7xL = -1L + 5l Reorder the terms: -5l + 5l + -2lx + 7xL = -1L + 5l Combine like terms: -5l + 5l = 0 0 + -2lx + 7xL = -1L + 5l -2lx + 7xL = -1L + 5l Add '2lx' to each side of the equation. -2lx + 2lx + 7xL = -1L + 5l + 2lx Combine like terms: -2lx + 2lx = 0 0 + 7xL = -1L + 5l + 2lx 7xL = -1L + 5l + 2lx Add '-7xL' to each side of the equation. 7xL + -7xL = -1L + 5l + 2lx + -7xL Combine like terms: 7xL + -7xL = 0 0 = -1L + 5l + 2lx + -7xL Simplifying 0 = -1L + 5l + 2lx + -7xL 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.

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