log(6x-7)+log(x)=log(5)

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Solution for log(6x-7)+log(x)=log(5) equation: 


Simplifying
log(6x + -7) + log(x) = log(5)

Reorder the terms:
glo(-7 + 6x) + log(x) = log(5)
(-7 * glo + 6x * glo) + log(x) = log(5)
(-7glo + 6glox) + log(x) = log(5)

Multiply glo * x
-7glo + 6glox + glox = log(5)

Combine like terms: 6glox + glox = 7glox
-7glo + 7glox = log(5)

Reorder the terms for easier multiplication:
-7glo + 7glox = 5glo

Solving
-7glo + 7glox = 5glo

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.
-7glo + -5glo + 7glox = 5glo + -5glo

Combine like terms: -7glo + -5glo = -12glo
-12glo + 7glox = 5glo + -5glo

Combine like terms: 5glo + -5glo = 0
-12glo + 7glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-12 + 7x) = 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 '(-12 + 7x)' equal to zero and attempt to solve:

Simplifying
-12 + 7x = 0

Solving
-12 + 7x = 0

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

Add '12' to each side of the equation.
-12 + 12 + 7x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 7x = 0 + 12
7x = 0 + 12

Combine like terms: 0 + 12 = 12
7x = 12

Add '-7x' to each side of the equation.
7x + -7x = 12 + -7x

Combine like terms: 7x + -7x = 0
0 = 12 + -7x

Simplifying
0 = 12 + -7x

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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