Log 2 = 0.301 log 3 = 0.477 log 5 = 0.699 using this information find a) log 5/6= b) log 0.3 =

We want (a) log 5/6.  There's a rule of logs that states that

log a/b = log a - log b.  Here, log 5/6 = log 5 - log 6 = 0.699 - [log 2 + log 6].

This, in turn, is 0.699 - [0.301 + 0.477] = 0.699 - 0.778 = -0.079 = log 5/6.

Check:  does 10^(-0.079) = 0.834 = 5/6?  Yes, approximately.  5/6 = 0.33333...  

Also find (b) log 0.3.  log 0.3 = log 3/10 = log 3 - log 10 = log 3 - 1.

log 3 - 1 = 0.477 - 1.000 = -0.523.

Check:  Does 10^(-0.523) = 0.3?  YES