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If (log)4 5=aa n d(log)5 6=b , then (log...

If `(log)_4 5=aa n d(log)_5 6=b ,` then `(log)_3 2` is equal to `1/(2a+1)` (b) `1/(2b+1)` (c) `2a b+1` (d) `1/(2a b-1)`

A

` 1/(2a+1)`

B

` 1/(2b+1)`

C

` 2ab+1`

D

`1/(2ab-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Here, ` 5=4^(a) and 6=5^(b)`.
Let ` log_(3) 2=x," then "2 = 3^(x)`.
Now, ` 6 = 5^(b) = (4^(a))^(b) = 4^(ab) or 3 = 2^(2ab-1)`
`:. 2 = (2^(2ab-1))^(x) = 2^(x(2ab-1))`
` rArr x(2ab-1)=1`
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