log(5)*(x+20)+log(5)*(x+120)=5

Solution for log(5)*(x+20)+log(5)*(x+120)=5 equation:

Simplifying
log(5)(x + 20) + log(5)(x + 120) = 5

Reorder the terms:
glo * 5(20 + x) + log(5)(x + 120) = 5

Reorder the terms for easier multiplication:
5glo(20 + x) + log(5)(x + 120) = 5
(20 * 5glo + x * 5glo) + log(5)(x + 120) = 5
(100glo + 5glox) + log(5)(x + 120) = 5

Reorder the terms:
100glo + 5glox + glo * 5(120 + x) = 5

Reorder the terms for easier multiplication:
100glo + 5glox + 5glo(120 + x) = 5
100glo + 5glox + (120 * 5glo + x * 5glo) = 5
100glo + 5glox + (600glo + 5glox) = 5

Reorder the terms:
100glo + 600glo + 5glox + 5glox = 5

Combine like terms: 100glo + 600glo = 700glo
700glo + 5glox + 5glox = 5

Combine like terms: 5glox + 5glox = 10glox
700glo + 10glox = 5

Solving
700glo + 10glox = 5

Solving for variable 'g'.

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

Reorder the terms:
-5 + 700glo + 10glox = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 700glo + 10glox = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 140glo + 2glox) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + 140glo + 2glox)' equal to zero and attempt to solve:

Simplifying
-1 + 140glo + 2glox = 0

Solving
-1 + 140glo + 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 + 140glo + 1 + 2glox = 0 + 1

Reorder the terms:
-1 + 1 + 140glo + 2glox = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 140glo + 2glox = 0 + 1
140glo + 2glox = 0 + 1

Combine like terms: 0 + 1 = 1
140glo + 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.