Logarithms

Cover Logarithms
Logarithms
H N Henry Nathan Wheeler
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321; (G) 0. 3321.
§ 19. Miscellaneous Problems and Examples.
1 . Given the exponential equation 20 = 2'' ; find x. By § 8 we have log 20 = a; X log 2 ;, ^ log20 ^ 1. 3010 * ' ^~ log 2 ~ 0. 3010' . • . Log X = log (log 20 ) — log (log 2 ) = log 1. 3010 -logo. 3010. Logl. 3010 = 0. 1143 logo. 3010 = 1. 4786 logo; =0. 6357 . -. A; = 4. 322.
We see from the definition of a logarithm (§ 1) that the above value of x is the logarithm of 20 to the base 2 ; . -. Iog2 20 = 4. 322.
We can in like manner w
...ork out, by the aid of common logarithms, the logarithms of all numbers to any base.
2. Find loggO. G.
Put 0. 6 = 2^; . -. Is logO. G =a; X log2; .^ logo. 6 ^ 1. 7782 ' ' '^~ iog2 ~ 0. 3010' In order to obtain the value of x from this equation, we must observe that the form 1. 7782, although sometimes convenient for purposes of addition and subtraction, is not 20 LOGARITHMS.
suitable for purposes of inultipliea, tion or division ; we will therefo]"c reduce it to its equivalent, -1 +0. 7782= -0.


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