log(x)+log(x-1)=log(20)

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Solution for log(x)+log(x-1)=log(20) equation: 


Simplifying
log(x) + log(x + -1) = log(20)

Multiply glo * x
glox + log(x + -1) = log(20)

Reorder the terms:
glox + glo(-1 + x) = log(20)
glox + (-1 * glo + x * glo) = log(20)
glox + (-1glo + glox) = log(20)

Reorder the terms:
-1glo + glox + glox = log(20)

Combine like terms: glox + glox = 2glox
-1glo + 2glox = log(20)

Reorder the terms for easier multiplication:
-1glo + 2glox = 20glo

Solving
-1glo + 2glox = 20glo

Solving for variable 'g'.

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

Add '-20glo' to each side of the equation.
-1glo + -20glo + 2glox = 20glo + -20glo

Combine like terms: -1glo + -20glo = -21glo
-21glo + 2glox = 20glo + -20glo

Combine like terms: 20glo + -20glo = 0
-21glo + 2glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-21 + 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 '(-21 + 2x)' equal to zero and attempt to solve:

Simplifying
-21 + 2x = 0

Solving
-21 + 2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + 2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2x = 0 + 21
2x = 0 + 21

Combine like terms: 0 + 21 = 21
2x = 21

Add '-2x' to each side of the equation.
2x + -2x = 21 + -2x

Combine like terms: 2x + -2x = 0
0 = 21 + -2x

Simplifying
0 = 21 + -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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