if,a=log(10/9),b=log(25/24),c=log(81/80)
show that log2=7a-2b+3c

Use your log laws to break it up and simplify in terms of log(2), log(3), log (5). Everything with cancel except for one little ol' log(2).

For instance, to break up log(25/24), we can write it as



Now, to proceed:






Now, put it altogether and whittle it down to log(2).