if log10 5=a and log10 3=b then:...

if `log_10 5=a` and `log_10 3=b` then:

` log_(30) 8 = (3(1-a))/(b+1) `

` log_(40)15= (a+b)/(3-2a)`

` log_(243) 32 = (1-a)/b`

none of these

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The correct Answer is:

A, B, C

(1) ` log_(30) 8 = (3log_(10)2)/(log_(10)5+log_(10) 3+log_(10)2)`
` = (3(1-log_(10)5))/(log_(10)5+log_(10)3+log_(10)2)`
` = (3(1-log_(10)5))/(1+log_(10)3) = (3(1-a))/(1+b)`
(2)` log_(40) 15=(log_(10)15)/(log_(10)40)`
` = (log_(10)3+log_(10)5)/(log_(10)5+3[1-log_(10)5])=(a+b)/(3-2a)`
(3) `log_(243)32 = (log_(10)2)/(log_(10)3)=(1-log_(10)5)/(log_(10)3) = (1-a)/b `

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