log[5](x+17)+log[5](x+117)=5

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Solution for log[5](x+17)+log[5](x+117)=5 equation: 


Simplifying
log[5](x + 17) + log[5](x + 117) = 5

Reorder the terms:
glo * 5(17 + x) + log[5](x + 117) = 5

Reorder the terms for easier multiplication:
5glo(17 + x) + log[5](x + 117) = 5
(17 * 5glo + x * 5glo) + log[5](x + 117) = 5
(85glo + 5glox) + log[5](x + 117) = 5

Reorder the terms:
85glo + 5glox + glo * 5(117 + x) = 5

Reorder the terms for easier multiplication:
85glo + 5glox + 5glo(117 + x) = 5
85glo + 5glox + (117 * 5glo + x * 5glo) = 5
85glo + 5glox + (585glo + 5glox) = 5

Reorder the terms:
85glo + 585glo + 5glox + 5glox = 5

Combine like terms: 85glo + 585glo = 670glo
670glo + 5glox + 5glox = 5

Combine like terms: 5glox + 5glox = 10glox
670glo + 10glox = 5

Solving
670glo + 10glox = 5

Solving for variable 'g'.

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

Reorder the terms:
-5 + 670glo + 10glox = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 670glo + 10glox = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 134glo + 2glox) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-1 + 134glo + 2glox)' equal to zero and attempt to solve:

Simplifying
-1 + 134glo + 2glox = 0

Solving
-1 + 134glo + 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 + 134glo + 1 + 2glox = 0 + 1

Reorder the terms:
-1 + 1 + 134glo + 2glox = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 134glo + 2glox = 0 + 1
134glo + 2glox = 0 + 1

Combine like terms: 0 + 1 = 1
134glo + 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.

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