log(x-4)+logx=log(5x-14)

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Solution for log(x-4)+logx=log(5x-14) equation: 


Simplifying
log(x + -4) + logx = log(5x + -14)

Reorder the terms:
glo(-4 + x) + logx = log(5x + -14)
(-4 * glo + x * glo) + logx = log(5x + -14)
(-4glo + glox) + logx = log(5x + -14)

Combine like terms: glox + glox = 2glox
-4glo + 2glox = log(5x + -14)

Reorder the terms:
-4glo + 2glox = glo(-14 + 5x)
-4glo + 2glox = (-14 * glo + 5x * glo)
-4glo + 2glox = (-14glo + 5glox)

Solving
-4glo + 2glox = -14glo + 5glox

Solving for variable 'g'.

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

Add '14glo' to each side of the equation.
-4glo + 14glo + 2glox = -14glo + 14glo + 5glox

Combine like terms: -4glo + 14glo = 10glo
10glo + 2glox = -14glo + 14glo + 5glox

Combine like terms: -14glo + 14glo = 0
10glo + 2glox = 0 + 5glox
10glo + 2glox = 5glox

Add '-5glox' to each side of the equation.
10glo + 2glox + -5glox = 5glox + -5glox

Combine like terms: 2glox + -5glox = -3glox
10glo + -3glox = 5glox + -5glox

Combine like terms: 5glox + -5glox = 0
10glo + -3glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(10 + -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 '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Add '3x' to each side of the equation.
-3x + 3x = -10 + 3x

Combine like terms: -3x + 3x = 0
0 = -10 + 3x

Simplifying
0 = -10 + 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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