think outside box

6.75=27/4 so: log 6.75=log 27/4 log 27/4=log 27 - log 4 log 27=3log 3= 1.4313 log 4=2log 2 but log 10= log 2x5=1 log 2+log 5 = 1 so: log 2 = 0.3010 then 2 log 2= 0.6020 so: log 6.75=1.4313 - 0.6020=0.8293

$6.75 = \frac{675}{100} = \frac{3^3 \times 5^2}{100}$

$log 6.75 = log \frac{3^3 \times 5^2}{100} = 3 log 3 + 2 log 5 - log 100 = 3 \times 0.4771 + 2 \times 0.6990 - 2$