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If log(10) 2 = a, log(10)3 = b" then "l...

If ` log_(10) 2 = a, log_(10)3 = b" then "log_(0.72)(9.6)` in terms of a and b is equal to

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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CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
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