Question

Show that log 1000 is rational

Answer 1

Step-by-step explanation:

We Know that:-

(10)³=1000 and 3 is a Rational number.

To Prove:-

㏒₁₀1000 is a rational number.

Proof:-

㏒₁₀1000

㏒₁₀(10)³

3㏒₁₀10

3

As we know that 3 is a rational number.

∴ ㏒1000 is a rational number.

(Note:- If there is no Base in log then We use base 10 in preference to the log base e or natural logs because we live in a 10- based world and in some ways it make the numbersome out much more handily. Its just a scale factor away from base e.)