Great work anon.    

I'm just going to look at it a slightly different way. 

You beat me Alan.   

2log25 - 3log5 + log20 =

2 log (5*5) -3 log 5 + log (2*2*5)

We know that: log (a*b)= log a + log b:

2 (log 5 + log 5) -3 log 5 + log 2 + log 2 + log 5=

4 log 5 - 3 log 5 +log 5 + 2 log 2=

2 log 5 + 2 log 2

You can take it just a little further Anonymous:

2log(5) + 2log(2) = log(5²) + log(2²) = log(25) + log(4) = log(25*4) = log(100) = 2 (assuming log to the base ten)

We have

2log25 - 3log5 + log20

2log(5*5) - 3log 5 + log (4*5)

2log 5 + 2log 5 - 3log 5 + log4 + log 5      combine like terms

5log5 - 3log 5 + log4 =

2log5 + log 4 =

log5² + log 4 =

log 25 + log 4 =

log (25*4) =

log 100 =

2

We have confirmed it ......the answer is   2 !!!!!!!