Question

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

Answer 1

Answer:

1. Assume that log 2 is rational, that is,

                                         (1)

                where p, q are integers.

                Since log 1 = 0 and log 10 = 1,  0 < log 2 < 1  and therefore p < q.

                From (1),          

                                                

                                                   , 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

2.??????

sorry I know only first one

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Answer 2

Answer:

Assume that log 2 is rational, that is,

(1)

where p, q are integers.

Since log 1 = 0 and log 10 = 1, 0 < log 2 < 1 and therefore p < q.

From (1),

, 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.

Step-by-step explanation:

Assume that log 2 is rational, that is,

(1)

where p, q are integers.

Since log 1 = 0 and log 10 = 1, 0 < log 2 < 1 and therefore p < q.

From (1),

, 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.

log100=x

10².=10 ^x(power x)

x=2

therefor it is rational