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If 2a×5b=500,2^a × 5^b = 500,2a×5b=500, and a and b are integers, then a + b is ​
Question

If 2a×5b=500,2^a × 5^b = 500, and a and b are integers, then a + b is ​

A.

5

B.

6

C.

7

D.

Interminable 

Correct option is A

Given:
We are given:

 2a×5b=500,2^a × 5^b = 500,​ where a and b are integers.
We are to find the value of a + b.

Solution:
Step 1: Prime factorize 500
500 = 2 × 250
= 2 × 2 × 125
= 2² × 5³

So,
2a×5b2^a × 5^b​ = 2² × 5³

Thus,
a = 2, b = 3

Now:
a + b = 2 + 3 = 5

Final Answer:
S. Ans. (A) 5

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