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Problem 4. Prove that log, 11 is irrational (15 pts) Answer:

User Dekauliya
by
8.2k points

1 Answer

3 votes

Answer and explanation:

To prove :
\log_2 11 is irrational ?

Proof :

Let
\log_2 11 is rational number.

So, It can be expressed in p/q form where, p and q are integers and q is non-zero.


\log_2 11=(p)/(q)

Using property of logarithm,


11=(2)^{(p)/(q)}

or
11^q=(2)^(p)

Which means 11 must be divisible by 2 for some p and q,

But 11 and 2 are co-prime.

So, Our assumption is not true.


\log_2 11 is irrational number.

Hence proved.

User StaxMan
by
7.9k points

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