Match the following List I to List II

Answer

`a to q; b to p, s; c to p; d to p, r`

Explanation

a. `2^(log_((2sqrt2))15)=2^(log_(2^(3//2))15)=2^(2//3 log_(2)15)=2^(log_(2)15^(2//3)) = 15^(2//3)`
b. ` root(3)((5^(1//log_(7)5)+1/sqrt((-log_(10)0.1))))`
` = root(3)((5^(log_(5)7)1/sqrt((log_(10)0.1^(-1)))))`
` root(3)((7+1/sqrt(log_(10)10)))=root(3)((7+1))=2`
c. `log_(3)5*log_(25)27`
` = (log 5 log 27)/(log 3 log 25)=(log 5)/(log 3) xx 3/2 (log 3)/(log 5) 3/2 `
d. ` (log_(10)x)^(2) = log 100x = 2 + log_(10) x`
`"Putting "log x = t," we get " t^(2) = 2 + t`
` or t^(2)- t - 2 = 0`
` rArr t = 2 or t = - 1`
` rArr log_(10) x = 2 or log_(10) x =- 1`
` rArr x = 100 or x = 1//10`
Hence, the product of roots is 10.