Question

Find the value of p, if  \({\log _7}\sqrt {7\sqrt {7\sqrt {7\sqrt {.........\infty } } } } = p\).

1. 7
2. 1
3. 2
4. 3

Answer 1

Correct Answer - Option 2 : 1

CONCEPT:

• Log _x (x) = 1

 

CALCULATION:

Given \({\log _7}\sqrt {7\sqrt {7\sqrt {7\sqrt {.........\infty } } } } = p\)

Let  \(\sqrt {7x} = x\)

On squaring we get - 

7x = x²

⇒ x = 7

So, log ₇7 = 1

⇒  p = 1

Therefore, option (2) is the correct answer.