The number {log _2}7 is | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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\

Vedclass · Accepted Answer

An irrational number

Vedclass · Answer

(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.

The number ${\log _2}7$ is

Similar Questions

The sum of all the natural numbers for which $log_{(4-x)}(x^2 -14x + 45)$ is defined is -

If ${\log _{\tan {{30}^ \circ }}}\left( {\frac{{2{{\left| z \right|}^2} + 2\left| z \right| - 3}}{{\left| z \right| + 1}}} \right)\, < \, - 2$ then

Which is the correct order for a given number $\alpha $in increasing order

If ${\log _{10}}3 = 0.477$, the number of digits in ${3^{40}}$ is

If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to