- Home
- Standard 11
- Mathematics
Basic of Logarithms
easy
${\log _2}7$ એ . . . . થાય.
A
પૃણાંક
B
સંમેય સંખ્યા
C
અસંમેય સંખ્યા
D
અવિભાજ્ય સંખ્યા
(IIT-1990)
Solution
(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.
Standard 11
Mathematics
