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If 7^(a^(b))=2401 where a and b positive...

If `7^(a^(b))=2401` where a and b positive integers and `a ne 1`, then which of the following is (are). Correct ?
`I,a=b`
`II.agtb`
`III.altb`

A

Either I and III

B

Either II and III

C

Either I or III

D

I only

Text Solution

Verified by Experts

The correct Answer is:
C
Given `a ne 1.7^(a^(b))=2401` , it can be written in the following ways.
`7^(4^(1))=2401` , "in the case" `agt b`.
`7^(2^(2))= 2401`, in the case ` a=b`.
Either `agt b or a=b`.
Hence the correct option is (c).
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