log(x+1)+log(x-2)=log(x+6)

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Solution for log(x+1)+log(x-2)=log(x+6) equation:


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

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

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

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

Combine like terms: 1glo + -2glo = -1glo
-1glo + glox + glox = log(x + 6)

Combine like terms: glox + glox = 2glox
-1glo + 2glox = log(x + 6)

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

Solving
-1glo + 2glox = 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.
-1glo + -6glo + 2glox = 6glo + -6glo + glox

Combine like terms: -1glo + -6glo = -7glo
-7glo + 2glox = 6glo + -6glo + glox

Combine like terms: 6glo + -6glo = 0
-7glo + 2glox = 0 + glox
-7glo + 2glox = glox

Add '-1glox' to each side of the equation.
-7glo + 2glox + -1glox = glox + -1glox

Combine like terms: 2glox + -1glox = 1glox
-7glo + 1glox = glox + -1glox

Combine like terms: glox + -1glox = 0
-7glo + 1glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(-7 + 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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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