log(4)=log(x)+log(13-3x)

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Solution for log(4)=log(x)+log(13-3x) equation: 


Simplifying
log(4) = log(x) + log(13 + -3x)

Reorder the terms for easier multiplication:
4glo = log(x) + log(13 + -3x)

Multiply glo * x
4glo = glox + log(13 + -3x)
4glo = glox + (13 * glo + -3x * glo)
4glo = glox + (13glo + -3glox)

Reorder the terms:
4glo = 13glo + glox + -3glox

Combine like terms: glox + -3glox = -2glox
4glo = 13glo + -2glox

Solving
4glo = 13glo + -2glox

Solving for variable 'g'.

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

Add '-13glo' to each side of the equation.
4glo + -13glo = 13glo + -13glo + -2glox

Combine like terms: 4glo + -13glo = -9glo
-9glo = 13glo + -13glo + -2glox

Combine like terms: 13glo + -13glo = 0
-9glo = 0 + -2glox
-9glo = -2glox

Add '2glox' to each side of the equation.
-9glo + 2glox = -2glox + 2glox

Combine like terms: -2glox + 2glox = 0
-9glo + 2glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-9 + 2x) = 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 '(-9 + 2x)' equal to zero and attempt to solve:

Simplifying
-9 + 2x = 0

Solving
-9 + 2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + 2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2x = 0 + 9
2x = 0 + 9

Combine like terms: 0 + 9 = 9
2x = 9

Add '-2x' to each side of the equation.
2x + -2x = 9 + -2x

Combine like terms: 2x + -2x = 0
0 = 9 + -2x

Simplifying
0 = 9 + -2x

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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