Question

9. Is (i) log 2 rational or irrational? Justify your answer.
(ii) log 100 rational or irrational? Justify your answer.​

Answer 1

Answer:

Assume that log 2 is rational, that is,

log2=p/q

where p, q are integers. Since log 1=0 and log10=1,0<log2<1  and p<q.

2=10^p/q

2^p=(2*5)^q

2^q-p=5^p

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.

log 100 is rational . the reason is

log 100 = log 10 ^2

= 2 log 10

=2 ( since log 10=1)

therefore log 100 = 2 ,which is a rational number

Step-by-step explanation:

Answer 2

Answer:

(i) log 2 is an irrational number

because of log 2 is 0.301029995

(ii) log 100 is an rational number

because of log 100 is 2