logarithm trouble

log √[5x] + log √[20x]

Note that we can use the properties   

log a  + log b  = log [ a * b ]           and  log a^b  = b*log a

So we can write

log √[5x] + log √[20x]   = 

log (5x)^1/2 + log (20x)^1/2  =  

(1/2)  [ log (5x)  + log (20x) ]  =

(1/2) [  log (5x  * 20x) ]  =

(1/2) log ( 100 x²)  =

log (100x²)^1/2  =

log  √ [ 100x² ]

log (10x)      which can also be simplified as  

log 10 + log x  =

1 + log x