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

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


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

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

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

Reorder the terms:
6glo + glox + glox = log(7)

Combine like terms: glox + glox = 2glox
6glo + 2glox = log(7)

Reorder the terms for easier multiplication:
6glo + 2glox = 7glo

Solving
6glo + 2glox = 7glo

Solving for variable 'g'.

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

Add '-7glo' to each side of the equation.
6glo + -7glo + 2glox = 7glo + -7glo

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

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

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-1 + 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 '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Add '-2x' to each side of the equation.
2x + -2x = 1 + -2x

Combine like terms: 2x + -2x = 0
0 = 1 + -2x

Simplifying
0 = 1 + -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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