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viji
Trkaccheda of x = Tex = log 3x, where the logarithm is to the base 3.
(iv) Caturthaccheda of a number is the number of times that it can be divided by 4. Thus
Caturtha-ccheda of s = Ce x = Log 45, where the logarithm is to the base 4.
The following results regarding logarithms have been used in the Dhavala: (1) Log (min) = log m - log n. (2) Log (m. n ) = log m + log n. ( 3 )3 2log m = m, where the logarithm is to the base 2. ( 4 )4 Log ( ** )2 = 2x log x. (5)5 Log log ( x ) = log x + 1 + log log , ( for the left side = log ( 2x log x)
= log x + log 2 + log log x
= log x + 1 + log log x. as log 2 to the base 2 is 1 ). ( 6 )6 Log ( x* )** = x* log xx (7) Let a be any number, then
1st vargita-samvargita of a = 24 = B say] 2nd vargita-samvargita of a = BB = y say ) 3rd vargita-samvargita of a = yy =D [ eay ) The Dhavala gives the following results7 -- (i) Log B = a log a (ii) Log log B = log a + log log a. (iii) log y = Blog B (iv) log log y = log B + log log B
= log a + log log a + a log a. (v) log D = y log y (vi) log log D = log y + log log y.
and so on. ( 8 )8 Log log D < B2
This inequality gives the inequality
Blog B + log B + log log B < B2
1. ibid p. 56. 2. ibid p. 60. 3, ibid p. 55. 4. ibid p. 21 ff. 5. 1. e. . 6. 1. c. It should be mentioned here that now here in the text are these logarithms restricted to be integral. The number x is any number. xx is the first vargita-samvargita rasi. and ( xx ** is the second vargita-samvargita rasi. 7. Dhavală III, p. 21-24. i .
. 8. ibid p. 24.
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