log(x+14)-log(2)=log(3x+6)

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Solution for log(x+14)-log(2)=log(3x+6) equation:


Simplifying
log(x + 14) + -1log(2) = log(3x + 6)

Reorder the terms:
glo(14 + x) + -1log(2) = log(3x + 6)
(14 * glo + x * glo) + -1log(2) = log(3x + 6)
(14glo + glox) + -1log(2) = log(3x + 6)

Reorder the terms for easier multiplication:
14glo + glox + -1 * 2glo = log(3x + 6)

Multiply -1 * 2
14glo + glox + -2glo = log(3x + 6)

Reorder the terms:
14glo + -2glo + glox = log(3x + 6)

Combine like terms: 14glo + -2glo = 12glo
12glo + glox = log(3x + 6)

Reorder the terms:
12glo + glox = glo(6 + 3x)
12glo + glox = (6 * glo + 3x * glo)
12glo + glox = (6glo + 3glox)

Solving
12glo + glox = 6glo + 3glox

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.
12glo + -6glo + glox = 6glo + -6glo + 3glox

Combine like terms: 12glo + -6glo = 6glo
6glo + glox = 6glo + -6glo + 3glox

Combine like terms: 6glo + -6glo = 0
6glo + glox = 0 + 3glox
6glo + glox = 3glox

Add '-3glox' to each side of the equation.
6glo + glox + -3glox = 3glox + -3glox

Combine like terms: glox + -3glox = -2glox
6glo + -2glox = 3glox + -3glox

Combine like terms: 3glox + -3glox = 0
6glo + -2glox = 0

Factor out the Greatest Common Factor (GCF), '2glo'.
2glo(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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