Logarithm 2 calculator finds the logarithm function result in base 2. Calculate log base 2 of a number….Log base 2 Values Tables.

log(3) = x/y where x and y are integers. Since 3 raised to any integer power is odd and 10 raised to any integer power is even and that a number cannot be both even and odd, this cannot be true! Hence, we have reached at a contradiction and so log(3) must be irrational.

In this short note we prove that logarithms of most integers are 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.

Root 3 is irrational is proved by the method of contradiction. If root 3 is a rational number, then it should be represented as a ratio of two integers. We can prove that we cannot represent root is as p/q and therefore it is an irrational number.

<span lang=”EN-US. As 2 is rational number, ∴ log 100 <b>is also rational.

Short proof of “log 2 is irrational” , 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.

The Fundamental Theorem of Arithmetic is that every integer is a product of primes.

It is a rational number.