log(x+9)-log(2)=log(2x+2)

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Solution for log(x+9)-log(2)=log(2x+2) equation:


Simplifying
log(x + 9) + -1log(2) = log(2x + 2)

Reorder the terms:
glo(9 + x) + -1log(2) = log(2x + 2)
(9 * glo + x * glo) + -1log(2) = log(2x + 2)
(9glo + glox) + -1log(2) = log(2x + 2)

Reorder the terms for easier multiplication:
9glo + glox + -1 * 2glo = log(2x + 2)

Multiply -1 * 2
9glo + glox + -2glo = log(2x + 2)

Reorder the terms:
9glo + -2glo + glox = log(2x + 2)

Combine like terms: 9glo + -2glo = 7glo
7glo + glox = log(2x + 2)

Reorder the terms:
7glo + glox = glo(2 + 2x)
7glo + glox = (2 * glo + 2x * glo)
7glo + glox = (2glo + 2glox)

Solving
7glo + glox = 2glo + 2glox

Solving for variable 'g'.

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

Add '-2glo' to each side of the equation.
7glo + -2glo + glox = 2glo + -2glo + 2glox

Combine like terms: 7glo + -2glo = 5glo
5glo + glox = 2glo + -2glo + 2glox

Combine like terms: 2glo + -2glo = 0
5glo + glox = 0 + 2glox
5glo + glox = 2glox

Add '-2glox' to each side of the equation.
5glo + glox + -2glox = 2glox + -2glox

Combine like terms: glox + -2glox = -1glox
5glo + -1glox = 2glox + -2glox

Combine like terms: 2glox + -2glox = 0
5glo + -1glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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