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There exist positive integers A, B and C...

There exist positive integers A, B and C with no common factors greater than 1, such that 1, such that `A log_(200) 5+ B log_(200) 2=C` The sum `A + B+ C` equals

A

5

B

6

C

7

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
`A log_(200)5+B log_(200)2=C`
`therefore A log 5+B log 2=C log 200 = C log(5^(2)2^(3))`
`therefore A log 5+B log 2=2C log 5+3C log 2`
`therefore A=2C` and B = 3C
For no common factor greater than 1, C = 1
`therefore A = 2 , B = 3`
`therefore A+B+C=6`
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