A) Consistent and a unique solution
B) Consistent and infinitely many solutions
C) Inconsistent
D) No solution
Correct Answer: A
Solution :
Given equations are \[\text{216 }=\text{ 192 }\times \text{ 1 }+\text{ 24}\] and \[\text{192 }=\text{ 24 }\times \text{ 8 }+\text{ }0\] Here \[{{6}^{x}}\] and \[{{6}^{x}}={{(2\times 3)}^{x}}={{2}^{x}}\times {{3}^{x}}\] \[\Rightarrow \] \[{{6}^{x}}\] Hence, the given equations have a unique solution and are consistent.
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