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

7log(10/9)-2log(25/24)+3log(81/80)

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

log(5^{2})-log(24)\Rightarrow 2log(5)-log(2^{3}\cdot 3)\Rightarrow 2log(5)-(3log(2)+log(3))

Now, to proceed:
7log(10/9)=7\left(log(5)+log(2)-2log(3)\right)

2log(25/24)=2\left(2log(5)-3log(2)-log(3)\right)

3log(81/80)=3\left(4log(3)-4log(2)-log(5)\right)

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