What is Logarithm? Logarithm table is very useful while doing scientific calculation

What is Logarithm?

Logarithm is the way by which complex multiplication and division can be accompanied with Logarithm table. It basically used for scientific calculations (Division and Multiplication). It works for the decimal number system.

Example

(2.3008*10²) *(4.3004*10³) =2.3008*4.3004*10⁵

2.3008*10³/4.30004*10²=2.3008*10/4.30004

Rather multiplying rational numbers as shown above, we can take log values of the number and add them in case of multiplication and subtract from one another in case of division. Finally fetch out the corresponding anti-log value, so you can get the result of the calculation.

HOW DOES IT WORK?

In general, it works on a simple logic. When the values are same and the values has some power value, then this is applied - In order to multiply two numbers (which has the same value but has some power value, then) we just need to add the power value. And in case of division it has to be subtracted by the denominator power value.

10²*10³ =10⁵

10³/10²=10¹ …. = 10

In order to make Logarithm table the power values of the base 10’s are tabulated for the whole number and corrections also tabulated for the rational value of the number. Let’s say I need to see the Log value of 2. Then the value obeys this,

Log 2= 0.3010

And 10^0.3010=2 (Approximately)

i.e., Anti-Log 0.3010 = 2

So the log values can be summed when the actual values needs to be multiplied. And in case of division, subtraction can be applied.

To define it simply

a=10^{log a}=Anti-Log(log a)

NOW let’s take up one Multiplication scenario

a*b

a=10^{log a}; b=10^{log b};

Therefore a*b is equals to 10^{log a} X 10^{log b}, hence

a*b = 10^{log a + log b}

And it is nothing but Anti-Log (log a + log b).

Lets write like this a*b = Anti-Log (log a + log b).

In the same way a/b = Anti-Log (log a - log b).

As said earlier in this article, generally logarithm is used for scientific calculations, it is known that scientific values are represented as follows,

x.xxxx * 10 ^{+/- xxx}

And it is obvious we just need to sum or subtract the power value of 10, and by using Log tables we can perform multiplication or division for the number. So we can just ignore the sections 10 ^{+/- xxx}of the scientific notation, because it is known that calculating this section as part of the arithmetic operation is easier.

If you look the logarithm table Log values are available for the range 1 to 99 and its rational values. And Anti-Log values also available only to comply that range.