is there any way of finding out the logarithm value of a number without using log tables?

Question

I want to findout the log value of a number say 45 without using the log tables?

Answer 1

CALCULATORS

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

1) A calculator.
2) Very impractical, but: First try to get the natural log of 45. Then by a certain constant.
To get the natural log of 45, draw a curve showing y = 1/x in the first quadrant, i.e. no minus numbers. Find the area under the curve between x=1 and x=45. That area is ln(45) i.e. log to the base e of 45. Divide your answer by ln(10) i.e. 2.3026 approximately.

Answer 4

Consider this : X ^a = Z

Similarly :
log[base x] (z) = a
// note x is the base and z is the number you wish to find the log of, and a is the power x was raised to in order to equal z. It is just another way of saying the above statement, in short.
So if its base is 10 we can omit writting it - it is implied.
log[base 5] (25)=2 // same as 5^2=25
log (100)=2 // same as 10^2 = 100

So when looking at a problem as yourself one question,
To what power was this based raised to get this number?
That is the log of that number.

Answer 5

There is. That is the way the log tables were made. It would be very difficult to do so.
But if you want to find log of some simple nos, you can do so by using properties of log.
By knowing log 2 & log 3 & log 7 you can find log of many numbers excluding prime nos.

Answer 6

log 45 = x;
10^x = 45.
solve for x (10 raised to what power will give you 45? about 1.65).

use: log a = b; 10^b = a formula
or use a calculator.

Answer 7

you can use Excel or your scientific calculator or you can estimate the value of a log number.

Answer 8

Have you heard of calculators?