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How to Use Logarithm and Antilogarithm Tables for Mathematics


How to Use Logarithm and Antilogarithm Tables for Mathematics




Logarithms and antilogarithms are mathematical functions that are useful for simplifying complex calculations. They can also help you find the power or exponent of a number. In this article, we will explain what logarithms and antilogarithms are, how to use them with tables, and how to convert them to Excel format.




Logarithm And Antilogarithm Table To Excel.pdf



What are Logarithms and Antilogarithms?




A logarithm is the inverse function of an exponentiation. It tells you what power you need to raise a base number to get another number. For example, the logarithm of 1000 to the base 10 is 3, because 10 = 1000. The notation for logarithms is logb(x), where b is the base and x is the number.


An antilogarithm is the inverse function of a logarithm. It tells you what number you get when you raise a base number to a power. For example, the antilogarithm of 3 to the base 10 is 1000, because 10 = 1000. The notation for antilogarithms is b, where b is the base and x is the power.


How to Use Logarithm and Antilogarithm Tables?




A logarithm table is a table that lists the logarithms of numbers from 1 to 10,000 to a certain base, usually 10. A logarithm table can help you find the logarithm of any number by using interpolation. For example, if you want to find the logarithm of 19.67 to the base 10, you can use the following steps[^1^]:


  • Identify the characteristic and the mantissa of the number. The characteristic is the integer part of the logarithm, which is equal to the number of digits before the decimal point minus one. The mantissa is the decimal part of the logarithm, which is always positive. For 19.67, the characteristic is 1 and the mantissa is unknown.



  • Look up the first two digits of the number (19) in the leftmost column of the table. Find the row that corresponds to these digits.



  • Look up the third digit of the number (6) in the top row of the table. Find the column that corresponds to this digit.



  • Find the intersection of the row and column from steps 2 and 3. This is an approximation of the mantissa of the logarithm.



  • Add a decimal point and two zeros to this approximation. For 19.67, this gives 0.2936.



  • Add or subtract a small correction factor from this approximation by using interpolation. The correction factor depends on the fourth digit of the number (7) and can be found in a separate table or by using a formula. For 19.67, this gives -0.0004.



  • Add the characteristic and the corrected mantissa to get the final answer. For 19.67, this gives log10(19.67) = 1 + 0.2936 - 0.0004 = 1.2932.



An antilogarithm table is a table that lists the antilogarithms of numbers from 0.00 to 0.99 to a certain base, usually 10. An antilogarithm table can help you find the antilogarithm of any number by using interpolation. For example, if you want to find


the antilogarithm of 1.2932 to the base 10, you can use


the following steps[^2^]:


Identify


the characteristic and


the mantissa


of


the number.


The characteristic


is


the integer part


of


the antilogarithm,


which


is equal


to


the power


of


the base.


The mantissa


is


the decimal part


of


the antilogarithm,


which


is always positive.


For


1.2932,


the characteristic


is e0e6b7cb5c


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