log[3](x-5)+log[3](x-11)=3

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Solution for log[3](x-5)+log[3](x-11)=3 equation:


Simplifying
log[3](x + -5) + log[3](x + -11) = 3

Reorder the terms:
glo * 3(-5 + x) + log[3](x + -11) = 3

Reorder the terms for easier multiplication:
3glo(-5 + x) + log[3](x + -11) = 3
(-5 * 3glo + x * 3glo) + log[3](x + -11) = 3
(-15glo + 3glox) + log[3](x + -11) = 3

Reorder the terms:
-15glo + 3glox + glo * 3(-11 + x) = 3

Reorder the terms for easier multiplication:
-15glo + 3glox + 3glo(-11 + x) = 3
-15glo + 3glox + (-11 * 3glo + x * 3glo) = 3
-15glo + 3glox + (-33glo + 3glox) = 3

Reorder the terms:
-15glo + -33glo + 3glox + 3glox = 3

Combine like terms: -15glo + -33glo = -48glo
-48glo + 3glox + 3glox = 3

Combine like terms: 3glox + 3glox = 6glox
-48glo + 6glox = 3

Solving
-48glo + 6glox = 3

Solving for variable 'g'.

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

Reorder the terms:
-3 + -48glo + 6glox = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -48glo + 6glox = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -16glo + 2glox) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + -16glo + 2glox)' equal to zero and attempt to solve: Simplifying -1 + -16glo + 2glox = 0 Solving -1 + -16glo + 2glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -16glo + 1 + 2glox = 0 + 1 Reorder the terms: -1 + 1 + -16glo + 2glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -16glo + 2glox = 0 + 1 -16glo + 2glox = 0 + 1 Combine like terms: 0 + 1 = 1 -16glo + 2glox = 1 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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