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Q.

 If 5 2x−1 − 25 x−1 =2500,   then what is the value of x?

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a

1 

b

3

c

8

d

5

answer is A.

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Detailed Solution

The given equation is,
5 2x−1 − 25 x−1 =2500  
To determine the value of x, we can simplify it as,
5 2x−1 − 25 x−1 =2500 ⇒ 5 2x−1 − 5 2x−2 =2500     a m n = a mn ⇒ 5 2x−2 5−1 =2500 ⇒ 5 2x−2 4 =2500 ⇒ 5 2x−2 =625  
⇒ 5 2x−2 = 5 4  
Comparing the exponents of both sides, we get,
2x−2=4 ⇒x=6 ⇒x=3  
Thus, the value of x is 3.
Hence, option 1 is the correct option.
 
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