How do you know if a log is irrational?

Theorem 1: The natural logarithm of every integer n ≥ 2 is an irrational number. Remark 1: It follows from the proof that for any base b which is a transcendental number the logarithm logb n of every integer n ≥ 2 is an irrational number.

How do you prove a contradiction is irrational?

The proof that √2 is indeed irrational is usually found in college level math texts, but it isn’t that difficult to follow. It does not rely on computers at all, but instead is a “proof by contradiction”: if √2 WERE a rational number, we’d get a contradiction….A proof that the square root of 2 is irrational.

2	=	(2k)2/b2
b2	=	2k2

Is log2 rational or irrational justify your answer?

Answer Expert Verified where q – p is an integer greater than 0. Now, it can be seen that the L.H.S. is even and the R.H.S. is odd. Hence there is contradiction and log 2 is irrational.

How do you prove log 7 is irrational?

We may assume that a>0 and b>0. We have 2a/b=7, which implies 2a=7b. But the number 2a is even and the number 7b is odd, a contradiction. Hence, log27 is irrational.

Is log 10 rational or irrational?

log10 5 is an irrational number. so there is no integer multiple of 5 equal to 3 and vice – versa. so our assumption is wrong. therefore, log10 5 is not a rational number.it is an irrational number.

Is log hundred rational or irrational?

As 2 is rational number, ∴ log 100 is also rational.

Is 3.27 a rational or irrational number?

3.27 bar is a rational number.

Is 8.27 rational or irrational justify your answer?

All decimals which terminate are rational numbers (since 8.27 can be written as 827100.) Decimals which have a repeating pattern after some point are also rationals: for example, 0.0833333….

Is log 7 rational or irrational?

This implies the same number has two different factorizations into prime numbers, which is impossible. So by contradiction, log_2 (7) can’t be rational.

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