log(x+8)+log(x)=log(x+18)

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Solution for log(x+8)+log(x)=log(x+18) equation:


Simplifying
log(x + 8) + log(x) = log(x + 18)

Reorder the terms:
glo(8 + x) + log(x) = log(x + 18)
(8 * glo + x * glo) + log(x) = log(x + 18)
(8glo + glox) + log(x) = log(x + 18)

Multiply glo * x
8glo + glox + glox = log(x + 18)

Combine like terms: glox + glox = 2glox
8glo + 2glox = log(x + 18)

Reorder the terms:
8glo + 2glox = glo(18 + x)
8glo + 2glox = (18 * glo + x * glo)
8glo + 2glox = (18glo + glox)

Solving
8glo + 2glox = 18glo + glox

Solving for variable 'g'.

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

Add '-18glo' to each side of the equation.
8glo + -18glo + 2glox = 18glo + -18glo + glox

Combine like terms: 8glo + -18glo = -10glo
-10glo + 2glox = 18glo + -18glo + glox

Combine like terms: 18glo + -18glo = 0
-10glo + 2glox = 0 + glox
-10glo + 2glox = glox

Add '-1glox' to each side of the equation.
-10glo + 2glox + -1glox = glox + -1glox

Combine like terms: 2glox + -1glox = 1glox
-10glo + 1glox = glox + -1glox

Combine like terms: glox + -1glox = 0
-10glo + 1glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-10 + 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 '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Add '-1x' to each side of the equation. x + -1x = 10 + -1x Combine like terms: x + -1x = 0 0 = 10 + -1x Simplifying 0 = 10 + -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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