log(x-17)-log(5)=log(x-8)-log(x)

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Solution for log(x-17)-log(5)=log(x-8)-log(x) equation:


Simplifying
log(x + -17) + -1log(5) = log(x + -8) + -1log(x)

Reorder the terms:
glo(-17 + x) + -1log(5) = log(x + -8) + -1log(x)
(-17 * glo + x * glo) + -1log(5) = log(x + -8) + -1log(x)
(-17glo + glox) + -1log(5) = log(x + -8) + -1log(x)

Reorder the terms for easier multiplication:
-17glo + glox + -1 * 5glo = log(x + -8) + -1log(x)

Multiply -1 * 5
-17glo + glox + -5glo = log(x + -8) + -1log(x)

Reorder the terms:
-17glo + -5glo + glox = log(x + -8) + -1log(x)

Combine like terms: -17glo + -5glo = -22glo
-22glo + glox = log(x + -8) + -1log(x)

Reorder the terms:
-22glo + glox = glo(-8 + x) + -1log(x)
-22glo + glox = (-8 * glo + x * glo) + -1log(x)
-22glo + glox = (-8glo + glox) + -1log(x)

Multiply glo * x
-22glo + glox = -8glo + glox + -1glox

Combine like terms: glox + -1glox = 0
-22glo + glox = -8glo + 0
-22glo + glox = -8glo

Solving
-22glo + glox = -8glo

Solving for variable 'g'.

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

Add '8glo' to each side of the equation.
-22glo + 8glo + glox = -8glo + 8glo

Combine like terms: -22glo + 8glo = -14glo
-14glo + glox = -8glo + 8glo

Combine like terms: -8glo + 8glo = 0
-14glo + glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-14 + x) = 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 '(-14 + x)' equal to zero and attempt to solve: Simplifying -14 + x = 0 Solving -14 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + x = 0 + 14 x = 0 + 14 Combine like terms: 0 + 14 = 14 x = 14 Add '-1x' to each side of the equation. x + -1x = 14 + -1x Combine like terms: x + -1x = 0 0 = 14 + -1x Simplifying 0 = 14 + -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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