log(x+5)-log(x+1)=log(3x)

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Solution for log(x+5)-log(x+1)=log(3x) equation: 


Simplifying
log(x + 5) + -1log(x + 1) = log(3x)

Reorder the terms:
glo(5 + x) + -1log(x + 1) = log(3x)
(5 * glo + x * glo) + -1log(x + 1) = log(3x)
(5glo + glox) + -1log(x + 1) = log(3x)

Reorder the terms:
5glo + glox + -1glo(1 + x) = log(3x)
5glo + glox + (1 * -1glo + x * -1glo) = log(3x)
5glo + glox + (-1glo + -1glox) = log(3x)

Reorder the terms:
5glo + -1glo + glox + -1glox = log(3x)

Combine like terms: 5glo + -1glo = 4glo
4glo + glox + -1glox = log(3x)

Combine like terms: glox + -1glox = 0
4glo + 0 = log(3x)
4glo = log(3x)

Remove parenthesis around (3x)
4glo = glo * 3x

Reorder the terms for easier multiplication:
4glo = 3glo * x

Multiply glo * x
4glo = 3glox

Solving
4glo = 3glox

Solving for variable 'g'.

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

Add '-3glox' to each side of the equation.
4glo + -3glox = 3glox + -3glox

Combine like terms: 3glox + -3glox = 0
4glo + -3glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(4 + -3x) = 0


Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve:

Simplifying
glo = 0

Solving
glo = 0

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

Simplifying
glo = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Add '3x' to each side of the equation.
-3x + 3x = -4 + 3x

Combine like terms: -3x + 3x = 0
0 = -4 + 3x

Simplifying
0 = -4 + 3x

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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