How to Find the Antilog of a Number

As you can guess from name, an antilog is the opposite of a logarithm. When you try to find the antilog of a number, you're basically looking for the number 10 with an exponent. So finding the antilog of 5 is the same as solving 10^5, or 100,000. When you have a really simple example like that, you can do the work in your head. If you're using a calculator, or if the example is not so simple, you have to follow a certain key pattern or look in a logarithm table. These are charts that people used to do logarithms before calculators came into use.

Things You'll Need

• Calculator or log base 10 tables

Instructions

Calculator

1. Input the number into the calculator.

2. Look at the calculator and find a button marked with "10^x." Some calculators have 10^x as a "second" function, written above another key -- usually the LOG key. If yours is like this, you should also see a button labeled "2nd" that allows you to access this second layer of commands. Individual calculators may have slightly different commands, but you'll see some sort of variation of LOG or 10^x.

3. Press the 10^x key, or press 2nd and then the key that has 10^x written above it.

Log Tables

1. Write the antilog in exponent form, such as 10^6.342.

2. Look at the log column in the table. In some tables, the columns are set up with a number on the left and its log on the right, so if you're finding the opposite, or antilog, look in the log column for the number you have. The number to the left is the antilog. Other tables, depending on the publisher, may have a simple column on the left with numbers like 1, 2 and 3, with a row at the top of decimals like 0.1, 0.2 and so on. Use these tables by combining the numbers on the left and on top; for example, if you're looking for 0.415, follow the row it's in to the left to find 2, and follow the column it's in up to 0.6. So the antilog of 0.415 is 2.6.

3. Break up the exponent into 6 and 0.342 if the numbers in the log area of the table don't exceed 1.0.

4. Find 10^6; this is 1,000,000. All you have to do is count out six zeroes to the right of the 1 to find this -- not 10, but 1. Remember that 10^1 is 10, or one zero to the right of the 1, if you get confused. If you were trying to find 10^8, that would be 1 followed by eight zeroes, or 100,000,000.

5. Look up the remaining portion of the exponent and find its antilog. Sometimes this is simple, and the exact number you need is listed in the table. Other times you might not find the exact number. In those cases, you may have to look for the closest number you can find, and estimate. For 0.342, the antilog is 2.2 if rounded to only one place to the right of the decimal.

6. Multiply together the two antilogs you found in Steps 4 and 5. In this example, 1,000,000 x 2.2 is 2,200,000. Note that rounding numbers up and down will affect the answer; if you double-check this on a calculator, your answer may be slightly different because the calculator will probably expand all numbers as far to the right of the decimal as it can.

Tips & Warnings

• Some log tables take shortcuts that could initially cause confusion. All the log amounts might not show decimal points in a table, for example, on the grounds that all those numbers are supposed to be to the right of a decimal point anyway, so the decimal is assumed.

References

• Lawrence Technological University: Logarithms to the Base 10; B. Chambers, et al.; 1996
• University of California, Santa Barbara: Math 34A: Anti-Logs
• "The Mechanical Engineer's Pocket-Book"; William Kent; 1903
• Bard College: Logarithms