how to find log of a number without using log table?

Answer 1

use calculator

Answer 2

I wouldn't recommend trying to do this by pen and paper arithmetic. It's very heavy work. Obviously the logarithms in tables of yesteryear were calculated by manual processes and/or large computers. The most elementary infinite series for calculating a logarithm is: log (base e) x = x - (x^3)/3 + (x^5)/5 - (x^7)/7 + ...... This converges extremely slowly because it contains no factorials and has alternating signs. It needs to be manipulated to converge much faster if it is to be used for practical purposes. For doing multiplication and division (as in the days before slide rules or calculators) you need logarithms to base 10, so that log 45 = log 4.5 + 1, log 450 = log 4.5 + 2 and so on. When you have your log to base e, you then need to use the relationship: log (base 10) x = log (base e) x * log (base 10) e where * denotes multiplication. Someone has already done all this for you, and built it into a microchip which you have in any scientific calculator. I hope this has given you some insight into what is involved, but this if far worse even than pen and paper calculation of square roots, another relic of mathematics which has now largely been consigned to the history books. If you really want to calculate just one log by yourself, choose a suitable number which bypasses all this work. log (base 10) 100 = 2, log (base 10) 10 = 1 and so on. Well, I always used to hate history, but then at school we only did the history of battles and religion. Mathematical history was never considered.

Answer 3

If you are doing natural logarithms, you can use the following formula:

ln[(1+x)/(1-x)]=2x+ (2/3)x^3+(2/5)x^5+....

For example, if you want to compute ln(5), you want
(1+x)/(1-x)=5, which gives x=2/3. Plug this value into
the sum on the right and use as many terms as you need
for the accuracy you desire.

There are a variety of tricks using the properties of logs
that allow you to use small values of x, for which fewer
terms are needed for accuracy. For example, with x=1/3,
you get ln(2) and for x=(1/2), you get ln(3). If you add the
results you get ln(6).

Of course, if you want to do common logs (i.e. base 10),
just use
log(x)=ln(x)/ln(10).

Of course, you can also use a calculator. There's one provided on your computer.

Answer 4

A calculator, or

An estimation using a Taylor or Maclaurin Series, see a calculus text.

Answer 5

use log chair.

Answer 6

use calculator