The rule is (log a to base b)*(log b to base a)=1 or log a to base b=1/(log b to base a). If a and b are replaced by 4 and 8, then your question becomes (log 8 to base 4)-1/(log 8 to base 4). We know that if we switch to base 2, we know that log 4 to base 2 is 2 and log 8 to base 2 is 3. Log 2 to base 4 therefore=1/(log 4 to base 2)=1/2. Log 8 to base 4=3(log 2 to base 4) because 8=2^3 and therefore log 8 to base 4=3/2 and log 4 to base 8=2/3. We have all we need to solve the problem: 3/2-2/3=5/6.