Logarithms, tables

Since it is possible to obtain logarithms by using hand calculators, this Handbook contains no logarithm tables. 

Use Kiister s logarithm tables. The limits of error are for carbon 0-3 per cent, for hydrogen +0-2 and - 0-1 per cent. Good analyses give about 0-1 per cent C too little and 0-1 per cent H too much. 

Every positive number has a logarithm. Numbers that are greater than 1 have a positive logarithm. Numbers that are between 0 and 1 have a negative logarithm. Table Dl gives some examples of the logarithm values of numbers. 

The mantissa of the logarithm of a number can be obtained from the logarithmic table. 

A part of the logarithmic table is given below (Difference to be added)... 

How to find the logarithm of a number from the logarithm table ... 

The antilogarithm tables are used in the same way as the logarithm tables. The only difference between the two tables is that the column at the extreme left of the log table contains all two digit numbers starting from 10 to 99 whereas an antilog table contains numbers from. 00 to. 99 (i.e., all fractional numbers with only two digits after decimal) in the extreme left column of it. 

Bowser s Five-Place Logarithmic Tables. 50cts. 

Wells s New Six-Place Logarithmic Tables. 60 cts. Pocket edition, small type 36 cts Wells s Four-Place Tables. 25 cts. 

To obtain the logarithm of a number other than an integral power of 10, you must use either an electronic calculator or a logarithm table. On most calculators, you do this by (1) entering the number and then (2) pressing the (log) button. 

Although it is possible to construct logarithm tables for the base e, or for any other base for that matter, there is a simple relationship between any two base systems such that a number found by the use of the common logarithmic table can easily be converted to the logarithm to any other base. Specifically, for the interconversion of common and natural logarithms, it can be shown that... 

Note that the logarithm of a logarithm must be taken if logarithm tables are used to perform this type of calculation. 

V. Numerical Values of hyperbolic functions.—Table IY. (pages 616, 617, and 618) contains numerical values of the hyperbolic sines and cosines for values of from 0 to 5, at intervals of 0 01. They have been checked by comparison with Des Ingenieurs Taschenbuch, edited by the Hiitte Academy, Berlin, 1877. The tables are used exactly like ordinary logarithm tables. Numerical values of the other functions can be easily deduced from those of sinh and cosh by the aid of equations (4). 

Table V. gives the value of log10r(w) to four decimal places for all values of n between 1 and 2. It has been adapted from Legendre s tables to twelve decimal places in his Exercises de Calcul Integral, Paris, 2, 18, 1817. For all values of n between 1 and 2, log T(w) will be negative. Hence, as in the ordinary logarithmic tables of the trigonometrical functions, the tabular logarithm is often increased by the addition of 10 to the logarithm of T(w). This must be allowed for when arranging the final result.

The problem resolves itself into the question What is the antilog of -2.7, or what is the numerical value of 10 raised to the power of -2.7 Your calculator should have a 10, or antilog key. It is used as follows first enter 2.7, then press the change sign key +/-. Next press the 10 key and read the answer, 0.002 M. If your calculator does not have an antilog function, do the calculation as described in Chap. 1 on the use of a logarithm table. 

A pH number is a logarithm. Table 17.4 shows the logarithms of 3.45 multiplied by five different powers of 10 0, 1, 2, 8, and 12. One column shows the value of the logarithm to seven decimals. Another shows the logarithms rounded off to the correct number of significant figures. Notice three things ... 

Logarithms that cannot be expressed as integral exponents are foimd in tables or on slide rules. Logarithmic tables present logarithms of numbers between 1 and 10 a decimal point is assumed to follow the... 

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