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wariber [46]
3 years ago
14

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

Mathematics
1 answer:
Licemer1 [7]3 years ago
5 0

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=\frac{p}{q}

Using property of logarithm,

11=(2)^{\frac{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.

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As per given , we have

p = 12%= 0.12

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Critical value for 95% confidence interval : z* = 1.960  [By z-table ]

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n=(0.1056)(78.4)^2

n=(0.1056)(6146.56)

n=649.076736\approx650

Thus , the required sample size = 650

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