Math, asked by eharinath, 1 year ago

log2 rational or irrational? Justify your answer.

Answers

Answered by vishwachaithanya
83
let us assume log 2 as rational,that is
  log 2=p/q -------1
where p,q are integers.
Since log 1 =0 and log 10=1,0<log 2<1 and therefore p<q.
from 1,   2=10powerp/q
              2powerq=(2*5)power p
           2power q-p= 5 power p, where q-p is an interger greater than 0.
Now it can be seen that L.H.S is even and the RHS is odd.Hence there is contradiction and therefore log2 is irrational.
Answered by kalyan639
43

Answer:

Irrational

Step-by-step explanation:

Let, log 2 base 10 = x

2=10 power x

This not true for any rational value of x

Therefore log 2 base 10 is an irrational number

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