Antilog table is used to find the anti-logarithm of a number. Antilog is a function that is the inverse of the log function. We know that we use the log table for doing math calculations easily without using a calculator. While doing the calculations, we apply the log first for the given expression, and after simplifying we should use the antilog table to find the antilog of the result that gives the simplified result of the given expression.
Logarithm And Antilogarithm Table To Excel.pdf
Antilog table gives the antilog of a positive or a negative number. Antilog is the inverse of the logarithmic function. i.e., if log x = y then x = antilog (y). i.e., if "log" moves from one side to the other side of the equation, it becomes an antilog. So
Taking log on both sides,log x = log (6.723 21.572)Using one of the properties of logarithms,log x = log 6.723 + log 21.572Using the log table,log x = 0.8276 + 1.334log x = 2.1616
The antilogarithm table gives the antilog of a positive or a negative number. Antilog table is used to find the anti-logarithm of a number. Antilog is a function that is the inverse of the log function.
The invention of logarithms was foreshadowed by the comparison of arithmetic and geometric series. In the simple table used above, the top line is a geometric series and the bottom line is an arithmetic series.
To obtain the Briggs or base 10 table, the calculation would be continued until X exceeded 10 and then the L scale adjusted so that at X = 10, L = 1.In addition to the discrete series procedure, Napier and Briggs suggested the calculation of logarithms by extracting roots of 10; i.e., log 10 = 0.5, log 101/4 = 0.25. This permits the n computation of the previous paragraph to be shortened, for the Briggs logarithm can be adjusted for by taking L = 0.25 for X = 101/4. Power series were not used in the initial construction of the tables. The power series for log(1 + x) and ex were only available in the 18th century and rigorously established in the early 19th century.
Logarithm tables Napier died in 1617. Briggs published a table of logarithms to 14 places of numbers from 1 to 20,000 and from 90,000 to 100,000 in 1624.Adriaan Vlacq published a 10-place table for values from 1 to 100,000 in 1628, adding the 70,000 values. Both Briggs and Vlacq engaged in setting up log trigonometric tables. Such early tables were either to 1/100 of a degree or to a minute of arc. In the 18th century tables were published for 10-second intervals, which were convenient for seven-place tables.
The availability of logarithms greatly influenced the form of plane and spherical trigonometry. Convenient formulas are ones in which the operations that depend on logarithms are done all at once. The recourse to the tables then consists of only two steps. One is obtaining logarithms, the other obtaining antilogs. The procedures of trigonometry were recast to produce such formulas.
In 102 = 100, the logarithm of 100 to the base 10 is 2, written as log10 100 = 2. Common logarithms use the number 10 as the base. Natural logarithms use the transcendental number e as a base. The first tables of logarithms were published independently by Scottish mathematician John Napier in 1614 and Swiss mathematician Justus Byrgius in 1620.
The problem in constructing a table of logarithms is to make the intervals between successive entries small enough for usefulness in calculating. Logarithm tables have been replaced by electronic calculators and computers with logarithmic functions. Each logarithm contains a whole number and a decimal fraction, called respectively the characteristic and the mantissa. In the common system of logarithms, the logarithm of the number 7 has the characteristic 0 and the mantissa .84510 and is written 0.84510. The logarithm of the number 70 is 1.84510, and the logarithm of the number 700 is 2.84510. The logarithm of the number .7 is -0.15490.
The first step in calculating the Geometric Mean using this method is to determine the logarithm of each data point using your calculator. Next, add all of the data point logarithms together and divide this sum by the number of data points (n). In other words, take the average of the logs. Next, convert this log average back to a base 10 number using the antilogarithm function key on the calculator.
For Method 2, as shown in the table above, you would calculate the weighted mean of the natural logarithms of the mid-point values, which in this case is 3.228. When the value is converted back to base 10, the geometric mean is 25.221.
For information on how to use log tables, in abelard's page about writing down logarhitms. For information on why log tables are used, part of abelard's page on orders of magnitude, indices (powers) and logarithms 2ff7e9595c
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