if `log_10 5=a` and `log_10 3=b` then:A. ` log_(30) 8 = (3(1-a))/(b+1) `B. ` log_(40)15= (a+b)/(3-2a)`C. ` log_(243) 32 = (1-a)/b`D. none of these

if `log_10 5=a` and `log_10 3=b` then:A. ` log_(30) 8 = (3(1-a))/(b+1)

1.	if `log_10 5=a` and `log_10 3=b` then:A. ` log_(30) 8 = (3(1-a))/(b+1) `B. ` log_(40)15= (a+b)/(3-2a)`C. ` log_(243) 32 = (1-a)/b`D. none of these
Answer» Correct Answer - 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 `