How to Use Logarithmic Tables. Before computers and calculators, logarithms were quickly calculated using logarithmic. shall have all the conyeniences iamiliar to those who use German tables. . gives the logarithms of all entire numbers from 1 to ; each logarithm being. A logarithm for which the base is not specified (y = log x) is always power rules to separate all of the factors and use the table for log 1 to log 10 to evaluate.

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Find logarithm of the number17 of base 17 = ×10 .. If the corresponding degree value is less than (=1/), Use this formula. (A. on log tables, using them to find logs and antilogs (inverse logs), and . my worst enemy to have to learn about logarithms the way I did, using log tables to find. There are many methods but we are going to use a convenient one. Note: Here, we are going to find the log of some number with base Let's find the log of.

Now I'll teach you antilogs, with another golden example. Calculate Antilog Now to do this, But is it possible to calculate it directly? Of-course not. Note: In Antilogs, we use non-scientific notation, but get the answer in scientific notation. Note: Tables give "Base to" 10 remember!

Therefore, answer is: 2. I've also summed up the important points mentioned earlier, so that you may not need to list them separately. Procedure followed to get the values of logs, antilogs, sines, tangents, cotangets, etc. Logarithms can't be negative, whereas Antilogarithms can have negative values.

And generally, the opposite is true for their answers. While calculating Logs not Antilogs! In Antilogs, we use non-scientific notation, but get the answer in scientific notation. For Your finger is currently on row 15 and column 2. Slide it over to row 15 and mean differences column 7. Add the numbers found in the two preceding steps together. This is the mantissa of the logarithm of Add the characteristic. Since 15 is between 10 and 10 1 and 10 2 , the log of 15 must be between 1 and 2, so 1.

Combine the characteristic with the mantissa to get your final answer. Find that the log of Method 3. Understand the anti-log table. Use this when you have the log of a number but not the number itself. If you have x, find n using the log table.

If you have n, find x using the anti-log table. The anti-log is also commonly known as the inverse log. Write down the characteristic. This is the number before the decimal point.

If you're looking up the anti-log of 2. Mentally remove it from the number you're looking up, but make sure to write it down so you don't forget it - it will be important later. Find the row that matches the first part of the mantissa.

Most anti-log tables, like most log tables, have two digits in the leftmost column, so run your finger down that column until you find. Slide your finger over to the column marked with the next digit of the mantissa.

For 2. This should read If your anti-log table has a table of mean differences, slide your finger over to the column in that table marked with the next digit of the mantissa. Make sure to keep your finger in the same row. In this case, you will slide your finger over to the last column in the table, column 9.

The intersection of row. Write that down. Add the two numbers from the two previous steps. In our example, these are and Add them together to get Use the characteristic to place the decimal point. Our characteristic was 2. This means that the answer is between 10 2 and 10 3 , or between and In order for the number to fall between and , the decimal point must go after three digits, so that the number is about rather than 70, which is too small, or , which is too big.

So the final answer is Method 4. Understand how to multiply numbers using their logarithms. So, the sum of the logarithms of two different numbers is the logarithm of the product of those numbers.

We can multiply two numbers of the same base by adding their powers. Look up the logarithms of the two numbers you want to multiply. Use the method above to find the logarithms. For example, if you want to multiply Add the two logarithms to find the logarithm of the solution. In this example, add 1. This number is the logarithm of your answer.

Look up the anti-logarithm of the result from the above step to find the solution. You can do this by finding the number in the body of the table closest to the mantissa of this number The more efficient and reliable method, however, is to find the answer in the table of anti-logarithms, as described in the method above.

For this example, you will get Yes No. Not Helpful 7 Helpful Multiply 3. Now, divide this by 10 to get your log with base Not Helpful 11 Helpful Say you want to find the log of 9.

Now that you have the correct number of significant digits, you can use a log table as long as you deal with decimal points correctly. Not Helpful 35 Helpful You now have enough significant digits to follow method 2 in the article. Not Helpful 22 Helpful As long as the quotient is an exponent, you can use the normal method to find the antilog.

Not Helpful 23 Helpful Then add 3 as is between and Answer is 3. Not Helpful 12 Helpful Choose the base you want to use. Write the numbers down the left side and the numbers across the top. Use a calculator or spreadsheet to calculate the log for each space in the table. Not Helpful 28 Helpful You can express this as 46 x 10 to the power The next step is to find log 46 , then multiply it with 10 to the power Not Helpful 24 Helpful Balaaji Selvanathan.

Not Helpful 43 Helpful Joab Kalyegira. Express the log as negative characteristic minus the mantissa Also called the "characteristic". The "characteristic" is 1. The final answer is 1. Just count the digits left of the decimal and subtract one. Method 2. Understand what a logarithm is. The powers 2 and 3 are the base logarithms of and So, saying "ten to the power of two is " is equivalent to saying "the base-ten log of is two.

By far the most common type of log table uses base logs, also called the common logarithm. Multiply two numbers by adding their powers. For example: The natural log, represented by "ln", is the base-e log, where e is the constant 2.

This is a useful number in many areas of math and physics. You can use natural log tables in the same way that you use common, or base, log tables. Identify the characteristic of the number whose log you want to find. Let's say you want to find the base log of 15 on a common log table.

What comes before the decimal point 1 in the first example, 2 in the second is the characteristic. Slide your finger down to the appropriate row on the table using the leftmost column. This column will show the first two or, for some large log tables, three digits of the number whose logarithm you're looking up.

If you're looking up the log of If you're looking up the log of 2. Sometimes the numbers in this row will have a decimal point, so you'll look up 2. You can ignore this decimal point, as it won't affect your answer. Also ignore any decimal points in the number whose logarithm you're looking up, as the mantissa for the log of 1. On the appropriate row, slide your finger over to the appropriate column.

This column will be the one marked with the next digit of the number whose logarithm you're looking up. For example, if you want to find the log of Slide your finger along that row to the right to find column 2. You will be pointing at the number Write this down. If your log table has a mean difference table, slide your finger over to the column in that table marked with the next digit of the number you're looking up.

For Your finger is currently on row 15 and column 2. Slide it over to row 15 and mean differences column 7. Add the numbers found in the two preceding steps together. This is the mantissa of the logarithm of Add the characteristic. Since 15 is between 10 and 10 1 and 10 2 , the log of 15 must be between 1 and 2, so 1. Combine the characteristic with the mantissa to get your final answer.

Find that the log of Method 3. Understand the anti-log table. Use this when you have the log of a number but not the number itself. If you have x, find n using the log table. If you have n, find x using the anti-log table. The anti-log is also commonly known as the inverse log. Write down the characteristic. This is the number before the decimal point. If you're looking up the anti-log of 2. Mentally remove it from the number you're looking up, but make sure to write it down so you don't forget it - it will be important later.

Find the row that matches the first part of the mantissa.

Most anti-log tables, like most log tables, have two digits in the leftmost column, so run your finger down that column until you find. Slide your finger over to the column marked with the next digit of the mantissa. For 2. This should read If your anti-log table has a table of mean differences, slide your finger over to the column in that table marked with the next digit of the mantissa.

Make sure to keep your finger in the same row.

In this case, you will slide your finger over to the last column in the table, column 9. The intersection of row.

Write that down. Add the two numbers from the two previous steps. In our example, these are and Add them together to get Use the characteristic to place the decimal point.

Our characteristic was 2. This means that the answer is between 10 2 and 10 3 , or between and In order for the number to fall between and , the decimal point must go after three digits, so that the number is about rather than 70, which is too small, or , which is too big. So the final answer is Method 4. Understand how to multiply numbers using their logarithms.

So, the sum of the logarithms of two different numbers is the logarithm of the product of those numbers. We can multiply two numbers of the same base by adding their powers.

Look up the logarithms of the two numbers you want to multiply.

Use the method above to find the logarithms. For example, if you want to multiply Add the two logarithms to find the logarithm of the solution. In this example, add 1.