The number log_{2} 7 is: | vedclass

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Question

(C) Assume (if possible) that $\log_{2} 7 = \frac{p}{q}$ is a rational number,where $p$ and $q$ are coprime integers.Then $\frac{p}{q} = \log_{2} 7 \i

Vedclass · Accepted Answer

An irrational number

Vedclass · Answer

(C) Assume (if possible) that $\log_{2} 7 = \frac{p}{q}$ is a rational number,where $p$ and $q$ are coprime integers.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 even and the $R.H.S.$ is odd.Clearly,$\log_{2} 7$ is neither an integer nor a prime number. Therefore,it is an irrational number.

The number $\log_{2} 7$ is:

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