Which of the following, when simplified, reduces to unity? (a) `(log)_(10)5dot(log)_(10)20+((log)_(10)2)^2` (b) `(2log 2+ log 3)/(log 48-log 4)` . (c) `-(log)_5(log)_3sqrt(5sqrt(9))` (d) `1/6(log)_((sqrt(3))/2)((64)/(27))`

Explanation

a)`log_10^5*log_10^2+(log_10^2)^2`

`log_10 10/2 log_10^(10.2)+...`

`(1-log2)(1+log2)+(log2)^2`

`1-(log2)^2+(log2)^2=1`

b)`(2log2+log3)/(log48-log4)=(log4+log2)/(log48-log4)`

`(log4*3)/(log(48/4)=log12/log12=1`

c)`-log_5 log_3 (9^(1/5))^(1/2)`

`-log_5 log_3 3^(2/(5*2))`

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