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The number log2 (7) is...

The number `log_2 (7)` is

A

an integer

B

a rational number

C

an irrational number

D

a prime number

Text Solution

Verified by Experts

The correct Answer is:
C
Let `"log"_(2)7` be a rational number equal to `(m)/(n)`, where `m, n notin N` and they do not have a common factor. Then,
`"log"_(2) 7 = (m)/(n) rArr 7 = 2^(m//n) rArr 7^(n) = 2^(m)`
Clearly, this is impossible, because `7^(th)` is an natural number and `2^(nd)` is an even natural number.
Hence, `"log"_(2)7` is an irrational number.
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