Log(12)=log(x)+log(7-x)

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Solution for Log(12)=log(x)+log(7-x) equation:


Simplifying
Log(12) = log(x) + log(7 + -1x)

Reorder the terms for easier multiplication:
12goL = log(x) + log(7 + -1x)

Multiply glo * x
12goL = glox + log(7 + -1x)
12goL = glox + (7 * glo + -1x * glo)
12goL = glox + (7glo + -1glox)

Reorder the terms:
12goL = 7glo + glox + -1glox

Combine like terms: glox + -1glox = 0
12goL = 7glo + 0
12goL = 7glo

Solving
12goL = 7glo

Solving for variable 'g'.

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

Add '-7glo' to each side of the equation.
-7glo + 12goL = 7glo + -7glo

Combine like terms: 7glo + -7glo = 0
-7glo + 12goL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(-7l + 12L) = 0

Subproblem 1

Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(-7l + 12L)' equal to zero and attempt to solve: Simplifying -7l + 12L = 0 Reorder the terms: 12L + -7l = 0 Solving 12L + -7l = 0 Move all terms containing g to the left, all other terms to the right. Add '-12L' to each side of the equation. 12L + -12L + -7l = 0 + -12L Combine like terms: 12L + -12L = 0 0 + -7l = 0 + -12L -7l = 0 + -12L Remove the zero: -7l = -12L Add '7l' to each side of the equation. -7l + 7l = -12L + 7l Combine like terms: -7l + 7l = 0 0 = -12L + 7l Simplifying 0 = -12L + 7l 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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