Question

find out whether log8 32 is rational or irrational ? justify​

Answer 1

Answer:

i didn't understand that question

Answer 2

Answer:

\log 2log2 is an irrational number.

Step-by-step explanation:

To show : \log 2log2 is rational or irrational ?

Solution :

We assume that \log 2log2 is a rational number.

So, We can write \log 2log2 in form of p/q where p and q are integers and q is non-zero.

\log_{10} 2=\frac{p}{q}log

10

2=

q

p

We know, \log_b a=x\Rightarrow a=b^xlog

b

a=x⇒a=b

x

2=10^{\frac{p}{q}}2=10

q

p

2=(2\times 5)^{\frac{p}{q}}2=(2×5)

q

p

2^q=(2\times 5)^{p}2

q

=(2×5)

p

2^{q-p}=(5)^{p}2

q−p

=(5)

p

Where, q-p is an integer greater than zero.

Now, it can be seen that the L.H.S. is even and the R.H.S. is odd.

So, there is contradiction.

As \log 2log2 is an irrational number.

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