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in Logarithm by (24.0k points)
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The number log27 is :

(a) a prime number 

(b) a rational number 

(c) an irrational number 

(d) an integer

1 Answer

+1 vote
by (23.5k points)
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Best answer

(c) an irrational number

Let us assume log27 be a rational number. Then, 

log27 = \(\frac{p}{q}\),  where p,q ∈ I and q ≠ 0 

\(2^{\frac{p}{q}}\) = 7 ⇒ 2p = 7q 

This is not true as 2 is even and 7 is odd.

∴ Hence our assumption that log27 is a rational number is wrong. 

∴ log27 is an irrational number.

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