MCQ
The number ${\log _2}7$ is
- AAn integer
- BA rational number
- ✓An irrational number
- DA prime number
✓
Answer
Correct option: C.
An irrational number
c
(c) Suppose, if possible, ${\log _2}7$ is rational, say $p/q$ where $p$ and $q$ are integers, prime to each other.
(c) Suppose, if possible, ${\log _2}7$ is rational, say $p/q$ where $p$ and $q$ are integers, prime to each other.
Then, ${p \over q} = {\log _2}7\,\,\,\,\, \Rightarrow 7 = {2^{p/q}}\,\,\, \Rightarrow {2^p} = {7^q}$,
which is false since $L.H.S$ is even and $R.H.S$ is odd. Obviously ${\log _2}7$ is not an integer and hence not a prime number.
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