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​If 5n=625, then the value of n is:\text{If } \sqrt{5^n} = 625, \text{ then the value of } n \text{ is:}If 5n​
Question

If 5n=625, then the value of n is:\text{If } \sqrt{5^n} = 625, \text{ then the value of } n \text{ is:}​​​​

A.

8

B.

6

C.

7

D.

9

Correct option is A

Given:

5n\sqrt{5^n} = 625

Solution:

5n\sqrt{5^n} = 252​ 

5n\sqrt{5^n} = (52)2,    

5n\sqrt{5^n} = 54 

We do again squire both side 

(5n\sqrt{5^n})2 = (54)2 

5n = 58 

n = 8

Option (a)

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