Easiest way is to calculate log5 by referring to logarithmic tables, which shows log5=0.6990
Another way could be using log2=0.3010 (again for this we need log tables) as log5=log(10/2)=log10-log2=1-0.3010=0.6990
In fact one need to remember log (to the base 10) for first ten numbers and it makes things lot easier. Note that while log1=0, log10=1. In fact, you just need to know log2=0.3010, log3=0.4771 and log7=0.8451 and then all logs can be worked out using these as
log4=2log2,
log5=1-log2,
log6=log2+log3,
log8=3log2 and
log9=2log3
If you want to go further, you need to remember log11=1.0414, log13=1.1139, log17=1.2304 and log19=1.2788, rest can be easily calculated. For example log14=log2+log7=1.1461.
