________________
(3) The logarithm ( ardhaccheda ) or the logarithm of & logarithm ( ardhaccheda-salaka ) was used to reduce the consideration of big numbers to those of smaller ones, e. g.
(i) Logg 2 = 2 (ii) Log, log, 44 = 3, (iii) Log, log, 256256 =
11.
It is no wonder to find that today we take recourse to one or the other of the above three methods of expressing numbers. The decimal place-value notation has become the common property of all nations. Logarithms are used whenever cal. culations with big numbers have to be made. Instances of the use of the law of indices to express magnitudes in modern physics is common. For instance, the number of protons in the Universe has been calculated and expressed as
136.2256
And Skewes' number which gives information regarding the distribution of primes is expressed in the form--
All the above methods of expressing numbers have been used in the Dhavală. It follows that the methods were commonly knowa before the seventh century A. D. in India.
........
1. The number 136. 2256 expressed in the decimal notation is 15,747,724,136,275,002,577 605,653,961,181,555.468,044,717,914, 572,116,709,366,231,425,076,185,631,031,296. It will be observed that the third vargita-samvargita of 2, i. e., 256256 is greater than the number of protons in the Universe. If we imagine the entire Universe as a chess-board, and the protons in it as chessmen, and if we agree to call any interchange in the position of two protons a' move' in this cosmic game, then the total number of possible moves would be the number -
84 10 10
10
This number is also connected with the theory of the distribution of primes.
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