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How to Use Log and Antilog Tables to Find Logarithms and Antilogarithms of Numbers

Logarithms and antilogarithms are mathematical functions that are used to simplify calculations involving large numbers. Logarithms are the inverse of exponentiation, which means that they tell us what power we need to raise a base number to get another number. For example, log10 100 = 2, because 10 = 100. Antilogarithms are the inverse of logarithms, which means that they tell us what number we get when we raise a base number to a certain power. For example, antilog10 2 = 100, because 10 = 100.

However, finding logarithms and antilogarithms of numbers can be difficult without a calculator. That's why log and antilog tables are useful tools that can help us find these values quickly and easily. Log and antilog tables are tables that list the logarithms and antilogarithms of numbers with different bases, usually 10 or e (the natural logarithm base). By using these tables, we can find the logarithms and antilogarithms of numbers by looking up the corresponding values in the tables.

In this article, we will explain how to use log and antilog tables to find logarithms and antilogarithms of numbers with base 10. We will also provide you with a link to download a free PDF file of log and antilog tables that you can use for your calculations.

How to Use Log Tables to Find Logarithms of Numbers

To use log tables to find logarithms of numbers with base 10, we need to follow these steps:

Write the number in scientific notation, which means that we express it as a product of a decimal number between 1 and 10 and a power of 10. For example, 456 can be written as 4.56 x 10.

Separate the decimal part and the power of 10 part of the number. The decimal part is called the mantissa and the power of 10 part is called the characteristic. For example, for 4.56 x 10, the mantissa is 4.56 and the characteristic is 2.

Look up the mantissa in the log table and find its corresponding logarithm value. The log table usually has two columns: one for the first digit of the mantissa and one for the second digit of the mantissa. The rows are labeled with the third digit of the mantissa. For example, to find the logarithm of 4.56, we look at the column labeled 4 and the row labeled 6. The value in the intersection is 0.6598.

Add the characteristic to the logarithm value obtained from the log table. This is the final answer for the logarithm of the number. For example, log10 456 = log10 (4.56 x 10) = log10 4.56 + log10 10 = 0.6598 + 2 = 2.6598.

How to Use Antilog Tables to Find Antilogarithms of Numbers

To use antilog tables to find antilogarithms of numbers with base 10, we need to follow these steps:

Separate the integer part and the decimal part of the number. The integer part is called the characteristic and the decimal part is called the mantissa. For example, for 2.6598, the characteristic is 2 and the mantissa is 0.6598.

Look up the mantissa in the antilog table and find its corresponding antilogarithm value. The antilog table usually has two columns: one for the first digit of the mantissa and one for the second digit of the mantissa. The rows are labeled with the third digit 061ffe29dd