Logarithms antilogarithms

Donald E. Jones, Significant Digits in Logarithm Antilogarithm Interconversions, J. Chem. Educ. 49,753 (1972). 

An inverse logarithm (antilogarithm) is the number corresponding to a given logarithm. in general. 

The determination of logarithms and inverse logarithms (antilogarithms) is discussed in Appendix A. Significant figure rules for logarithms are also presented there. 

The common antilogarithm of a number x is the number that has x as its common logarithm. In practice, the common antilogarithm of x is simply another name for 10v, and so the common antilogarithm of 2 is 102 =100 and that of 2.18 is... 

In the conversion of a logarithm into its antilogarithm, the number of significant figures in the antilogarithm should equal the number of digits in the mantissa. Thus,... 

Mean of repeated measurements, calculated on a logarithmic basis. It has the advantage that extreme values do not influence the mean as is the case for an arithmetic mean. It can be calculated as the nth root of the product of the n values, and it can also be calculated as the antilogarithm of the mean of the logarithms of the n values. Volume 1(2). 

Problem 1 Explain the logarithmic and antilogarithmic relations with suitable examples. 

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. 

We could actually solve this sort of problem with just the pi-values and ignore the rest of the molecules. Notice that the difference in the two log Kov/ values is 2 x 0.71— 2 x (—0.02) = 1.46. Because this is a difference in logarithms, the antilogarithm (or exponentiation) of this difference is the factor by which the two values differ. Hence,... 

The following relations are presented to facilitate the use of natural and common logarithms, their antilogarithms, and exponential functions. For those readers who are completely unfamiliar with such quantities, a textbook or handbook should be consulted. 

EXAMPLE A.23. What sequence of keystrokes is required to determine (a) the logarithm of 1.15 and (b) the antilogarithm of 1.15 Reminder Some calculators require log to be entered before the number. Check the owner s manual. 

If one draws a scale on which logarithms go up by uniform steps, the antilogarithms will crowd closer and closer together as their size increases. They do this in a very systematic way. On a logarithmic scale, as this is called, equal intervals correspond to equal ratios. The interval between 1 and 2, for example, is the same length as the interval between 4 and 8. 

Thus, the absolute standard deviation of the logarithm of a number is determined by the relative standard deviation of the number conversely, the relative standard deviation of the antilogarithm of a number is determined by the absolute standard deviation of the number. Example 6-7 illustrates these calculations. 

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