`@Sun` 

`log_4 9 + log_(1/2) 5 - log_(2sqrt2) 6` 

`= log_(2^2) 9 +log_(2^(-1)) 5 - log_(2^(3/2)) 6` 

`= 1/2 log_2 9 - log_2 5 - 2/3 log_2 6` 

`= log_2 9^(1/2) + log_2 5^(-1) + log_2 6^(-2/3)` 

`=log_2 3 +( log_2) 1/5 + log_2 root{3}{6^(-2)}` 

`= log_2 3 + (log_2) 1/5 + log_2 root{3}{1/36}` 

 `= log_2 (3 . 1/5 . root{3}{1/36})` 

`= log_2 ( 3/5 . root{3}{1/36} )`