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#.
