log(x+18)-log(x)=log(x-6)

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Solution for log(x+18)-log(x)=log(x-6) equation:


Simplifying
log(x + 18) + -1log(x) = log(x + -6)

Reorder the terms:
glo(18 + x) + -1log(x) = log(x + -6)
(18 * glo + x * glo) + -1log(x) = log(x + -6)
(18glo + glox) + -1log(x) = log(x + -6)

Multiply glo * x
18glo + glox + -1glox = log(x + -6)

Combine like terms: glox + -1glox = 0
18glo + 0 = log(x + -6)
18glo = log(x + -6)

Reorder the terms:
18glo = glo(-6 + x)
18glo = (-6 * glo + x * glo)
18glo = (-6glo + glox)

Solving
18glo = -6glo + glox

Solving for variable 'g'.

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

Add '6glo' to each side of the equation.
18glo + 6glo = -6glo + 6glo + glox

Combine like terms: 18glo + 6glo = 24glo
24glo = -6glo + 6glo + glox

Combine like terms: -6glo + 6glo = 0
24glo = 0 + glox
24glo = glox

Add '-1glox' to each side of the equation.
24glo + -1glox = glox + -1glox

Combine like terms: glox + -1glox = 0
24glo + -1glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(24 + -1x) = 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 '(24 + -1x)' equal to zero and attempt to solve: Simplifying 24 + -1x = 0 Solving 24 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -1x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1x = 0 + -24 -1x = 0 + -24 Combine like terms: 0 + -24 = -24 -1x = -24 Add 'x' to each side of the equation. -1x + x = -24 + x Combine like terms: -1x + x = 0 0 = -24 + x Simplifying 0 = -24 + x 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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