log(5)(x+116)+log(5)(x+16)=5

Solution for log(5)(x+116)+log(5)(x+16)=5 equation:

Simplifying
log(5)(x + 116) + log(5)(x + 16) = 5

Reorder the terms:
glo * 5(116 + x) + log(5)(x + 16) = 5

Reorder the terms for easier multiplication:
5glo(116 + x) + log(5)(x + 16) = 5
(116 * 5glo + x * 5glo) + log(5)(x + 16) = 5
(580glo + 5glox) + log(5)(x + 16) = 5

Reorder the terms:
580glo + 5glox + glo * 5(16 + x) = 5

Reorder the terms for easier multiplication:
580glo + 5glox + 5glo(16 + x) = 5
580glo + 5glox + (16 * 5glo + x * 5glo) = 5
580glo + 5glox + (80glo + 5glox) = 5

Reorder the terms:
580glo + 80glo + 5glox + 5glox = 5

Combine like terms: 580glo + 80glo = 660glo
660glo + 5glox + 5glox = 5

Combine like terms: 5glox + 5glox = 10glox
660glo + 10glox = 5

Solving
660glo + 10glox = 5

Solving for variable 'g'.

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

Reorder the terms:
-5 + 660glo + 10glox = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 660glo + 10glox = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 132glo + 2glox) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + 132glo + 2glox)' equal to zero and attempt to solve:

Simplifying
-1 + 132glo + 2glox = 0

Solving
-1 + 132glo + 2glox = 0

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

Add '1' to each side of the equation.
-1 + 132glo + 1 + 2glox = 0 + 1

Reorder the terms:
-1 + 1 + 132glo + 2glox = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 132glo + 2glox = 0 + 1
132glo + 2glox = 0 + 1

Combine like terms: 0 + 1 = 1
132glo + 2glox = 1

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.