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Sets, Relations and Function - JEE Mathematics question (IIT-JEE 1990)

IIT-JEE 1990Question 1
The number $\log_{2}7$ is
Sets, Relations and Function
Options for question 1, choose one

Solution

If $\log_27=\frac pq$ then $2^p=7^q$, impossible (even vs odd). So $\log_27$ is irrational.

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