Correct Answer is : An irrational number

Indian Institute of Foreign Trade 2010 Solved Paper

Question : 18 of 135

Marks: +1, -0

\log_{5}2

Solution:

Let

\log_{5}2=y

Let us assume

\log_{5}2

is a rational number.

\log_{5}2=p{/}q

where p and q are co primes.

5^(p/q)=2=>5^p=2^q

5^p=5×5×5×5×5×5×5...........p

times

2^p=2×2×2×2×2×2×2..........

q times
No value of p and q can satisfy the equation. Hence y is an irrational number.

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