log(4-x)=log(x+8)+log(2x+13)

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Solution for log(4-x)=log(x+8)+log(2x+13) equation:


Simplifying
log(4 + -1x) = log(x + 8) + log(2x + 13)
(4 * glo + -1x * glo) = log(x + 8) + log(2x + 13)
(4glo + -1glox) = log(x + 8) + log(2x + 13)

Reorder the terms:
4glo + -1glox = glo(8 + x) + log(2x + 13)
4glo + -1glox = (8 * glo + x * glo) + log(2x + 13)
4glo + -1glox = (8glo + glox) + log(2x + 13)

Reorder the terms:
4glo + -1glox = 8glo + glox + glo(13 + 2x)
4glo + -1glox = 8glo + glox + (13 * glo + 2x * glo)
4glo + -1glox = 8glo + glox + (13glo + 2glox)

Reorder the terms:
4glo + -1glox = 8glo + 13glo + glox + 2glox

Combine like terms: 8glo + 13glo = 21glo
4glo + -1glox = 21glo + glox + 2glox

Combine like terms: glox + 2glox = 3glox
4glo + -1glox = 21glo + 3glox

Solving
4glo + -1glox = 21glo + 3glox

Solving for variable 'g'.

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

Add '-21glo' to each side of the equation.
4glo + -21glo + -1glox = 21glo + -21glo + 3glox

Combine like terms: 4glo + -21glo = -17glo
-17glo + -1glox = 21glo + -21glo + 3glox

Combine like terms: 21glo + -21glo = 0
-17glo + -1glox = 0 + 3glox
-17glo + -1glox = 3glox

Add '-3glox' to each side of the equation.
-17glo + -1glox + -3glox = 3glox + -3glox

Combine like terms: -1glox + -3glox = -4glox
-17glo + -4glox = 3glox + -3glox

Combine like terms: 3glox + -3glox = 0
-17glo + -4glox = 0

Factor out the Greatest Common Factor (GCF), '-1glo'.
-1glo(17 + 4x) = 0

Ignore the factor -1.

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 '(17 + 4x)' equal to zero and attempt to solve: Simplifying 17 + 4x = 0 Solving 17 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 4x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 4x = 0 + -17 4x = 0 + -17 Combine like terms: 0 + -17 = -17 4x = -17 Add '-4x' to each side of the equation. 4x + -4x = -17 + -4x Combine like terms: 4x + -4x = 0 0 = -17 + -4x Simplifying 0 = -17 + -4x 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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