A) a rational number such that \[0<x<2\]
B) an rational number
C) a rational number such that \[2<x<3\]
D) a prime number of the form \[7x+2\]
Correct Answer: B
Solution :
Suppose of possible \[{{\log }_{2}}7\]is rational say \[\frac{p}{q}\] where \[p\]and \[q\] are integers prime to each other then \[\frac{p}{q}={{\log }_{2}}7\Rightarrow {{2}^{p/q}}\Rightarrow {{2}^{p}}={{7}^{q}}.\] This is false because- L.H.S. is even where as the R.H.S. is odd.
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