Question

What is log5? How can we find logs of numbers without using a calculator?

Answer 1

log5=0.6990

Explanation:

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

$log5=\left(\frac{10}{2}\right)=log10-log2=1-0.3010=0.6990$

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.