Which of the following, when simplified, reduces to unity? `(log)_(10)5dot(log)_(10)20+((log)_(10)2)^2` . (c) `-(log)_5(log)_3sqrt(5sqrt(9))` `1/6(log)_((sqrt(3))/2)((64)/(27))`

Options

A. ` log_(10) 5 * log_(10) 20+(log_(10) 2)^(2)`
B. `(2 log 2+log 3)/(log 48 - log 4)`
C. ` - log_(5) log_(3) sqrtroot(5)9`
D. `1/6 log_(sqrt3//2)(64/27)`

Answer

A, B, C

Explanation

(1) ` log_(10)(10/2) * log_(10)(10xx2)+(log_(10)2)^(2)`
` = (1-log_(10)2)(1+log_(10)2)+(log_(10)2)^(2)=1`
(2) `(log2^(2)xx3)/(log(48//4)) = 1`
(3) ` -log_(5)log_(3)9^(1//10)=- log_(5)log_(3)3^(1//5)`
` = - log_(5)(1//5)=1`
(4) ` 1/4 log_(sqrt3/2)(64/27) = 1/6 log_(sqrt3/2)(sqrt3/2)^(-6)=- 1`