The number log_{2} 7 is | vedclass

Name: Exam Paper Generator | 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,$\frac{p}{q} = \log_{2} 7 \implies

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,$\frac{p}{q} = \log_{2} 7 \implies 7 = 2^{p/q} \implies 2^{p} = 7^{q}$.This is a contradiction because the $L.H.S$ is an even number (power of $2$) and the $R.H.S$ is an odd number (power of $7$).Since it cannot be expressed as a ratio of two integers,$\log_{2} 7$ is an irrational number.Obviously,$\log_{2} 7$ is not an integer and hence not a prime number.

The number $\log_{2} 7$ is

Similar Questions

If $\log_{5} a \cdot \log_{a} x = 2$,then $x$ is equal to

If ${\log _5}a \cdot {\log _a}x = 2$,then the value of $x$ is:

If $\alpha = \log_e(2+\sqrt{3})$,then $\frac{\cosh \alpha}{1-\tanh \alpha} + \frac{\sinh \alpha}{1-\coth \alpha} = $

If $\log _k x \cdot \log _5 k = \log _x 5$,where $k \ne 1$ and $k > 0$,then $x$ is equal to:

If $\log _{0.3}(x-1) < \log _{0.09}(x-1),$ then $x$ lies in the interval

Vedclass Test Series

Exam Paper Generator

Online Exam Module