log(x)+log(x-2)=log(120)

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Solution for log(x)+log(x-2)=log(120) equation:


Simplifying
log(x) + log(x + -2) = log(120)

Multiply glo * x
glox + log(x + -2) = log(120)

Reorder the terms:
glox + glo(-2 + x) = log(120)
glox + (-2 * glo + x * glo) = log(120)
glox + (-2glo + glox) = log(120)

Reorder the terms:
-2glo + glox + glox = log(120)

Combine like terms: glox + glox = 2glox
-2glo + 2glox = log(120)

Reorder the terms for easier multiplication:
-2glo + 2glox = 120glo

Solving
-2glo + 2glox = 120glo

Solving for variable 'g'.

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

Add '-120glo' to each side of the equation.
-2glo + -120glo + 2glox = 120glo + -120glo

Combine like terms: -2glo + -120glo = -122glo
-122glo + 2glox = 120glo + -120glo

Combine like terms: 120glo + -120glo = 0
-122glo + 2glox = 0

Factor out the Greatest Common Factor (GCF), '2glo'.
2glo(-61 + x) = 0

Ignore the factor 2.

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 '(-61 + x)' equal to zero and attempt to solve: Simplifying -61 + x = 0 Solving -61 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '61' to each side of the equation. -61 + 61 + x = 0 + 61 Combine like terms: -61 + 61 = 0 0 + x = 0 + 61 x = 0 + 61 Combine like terms: 0 + 61 = 61 x = 61 Add '-1x' to each side of the equation. x + -1x = 61 + -1x Combine like terms: x + -1x = 0 0 = 61 + -1x Simplifying 0 = 61 + -1x 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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