log[5](x)+log[5](x-24)=2

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Solution for log[5](x)+log[5](x-24)=2 equation: 


Simplifying
log[5](x) + log[5](x + -24) = 2

Reorder the terms for easier multiplication:
5glo * x + log[5](x + -24) = 2

Multiply glo * x
5glox + log[5](x + -24) = 2

Reorder the terms:
5glox + glo * 5(-24 + x) = 2

Reorder the terms for easier multiplication:
5glox + 5glo(-24 + x) = 2
5glox + (-24 * 5glo + x * 5glo) = 2
5glox + (-120glo + 5glox) = 2

Reorder the terms:
-120glo + 5glox + 5glox = 2

Combine like terms: 5glox + 5glox = 10glox
-120glo + 10glox = 2

Solving
-120glo + 10glox = 2

Solving for variable 'g'.

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

Reorder the terms:
-2 + -120glo + 10glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -120glo + 10glox = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -60glo + 5glox) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -60glo + 5glox)' equal to zero and attempt to solve:

Simplifying
-1 + -60glo + 5glox = 0

Solving
-1 + -60glo + 5glox = 0

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

Add '1' to each side of the equation.
-1 + -60glo + 1 + 5glox = 0 + 1

Reorder the terms:
-1 + 1 + -60glo + 5glox = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -60glo + 5glox = 0 + 1
-60glo + 5glox = 0 + 1

Combine like terms: 0 + 1 = 1
-60glo + 5glox = 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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