If (log)(10)2=a ,(log)(10)3=bt h e n(log...

If `(log)_(10)2=a ,(log)_(10)3=bt h e n(log)_(0. 72)(9. 6)` in terms of `aa n db` is equal to `(2a+3b-1)/(5a+b-2)` (b) `(5a+b-1)/(3a+2b-2)` (c) `(3a+b-2)/(2a+3b-1)` `(2a+5b-2)/(3a+b-1)`

A

`(2a+3b-1)/(5a+b-2)`

B

`(5a+b-1)/(3a+2b-2)`

C

`(3a+b-2)/(2a+3b-1)`

D

`(2a+5b-2)/(3a+b-1)`

Text Solution

Verified by Experts

The correct Answer is:

B

`log_(0.72)(9.6)= log_(72/100)(96/10) =((log_(10) 96-log_(10) 10))/((log_(10) 72 - log_(10)100))`
`=(log_(10)(2^(5)xx3)-1)/(log_(10)(2^(3)xx3^(2))-2)`
`=(5a+b-1)/(3a+2b-2)`

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