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# Log Table PDF: A Comprehensive Guide for Numbers 1 to 100

## What is a log table and why is it useful?

A log table is a table that lists the logarithms of numbers for a given base. A logarithm is the exponent or power that a base number must be raised to in order to get another number. For example, the logarithm of 1000 to the base 10 is 3, because 10 = 1000. The notation for this is log10(1000) = 3.

A log table is useful because it helps you find the logarithm of any number without using a calculator. This can save you time and effort when solving problems that involve exponential growth or decay, compound interest, pH levels, sound intensity, earthquake magnitude, and more. Log tables also help you compare the orders of magnitude of different numbers and understand the relationship between logarithmic and exponential functions.

### Definition and examples of logarithms

As mentioned above, a logarithm is the exponent or power that a base number must be raised to in order to get another number. The general form of a logarithm is:

logb(x) = y

This means that b = x, where b is the base, x is the number, and y is the logarithm. For example:

• log2(8) = 3, because 2 = 8

• log5(25) = 2, because 5 = 25

• log10(100) = 2, because 10 = 100

• loge(e) = 1, because e = e (e is the natural base, approximately equal to 2.718)

• log10(1) = 0, because 10 = 1 (any number raised to the power of zero is one)

• log10(0.01) = -2, because 10 = 0.01 (negative exponents mean reciprocal powers)

### Applications of logarithms in mathematics and science

Logarithms have many applications in mathematics and science, especially in fields that deal with exponential growth or decay, such as biology, chemistry, physics, astronomy, engineering, finance, and more. Some examples of applications are:

• Growth and decay models: Logarithms can be used to model the growth or decay of populations, bacteria, radioactive substances, drugs, etc. For example, if a population grows by a constant percentage every year, then the logarithm of the population size can be used to find the growth rate or the time required to reach a certain size. For example, if a population of 1000 grows by 5% every year, then the logarithm of the population size after t years is log10(1000) + 0.05t. To find how long it takes for the population to double, we can set log10(1000) + 0.05t = log10(2000) and solve for t, which gives t = 14.21 years.

• Compound interest: Logarithms can be used to calculate the amount of money that accumulates in an account that earns compound interest. For example, if an account has an initial balance of \$1000 and earns 10% interest compounded annually, then the balance after t years is 1000(1 + 0.1). To find how long it takes for the balance to reach \$2000, we can take the logarithm of both sides and get log10(1000(1 + 0.1)) = log10(2000), which simplifies to t = log10(2) / log10(1.1), which gives t = 7.27 years.

• pH levels: Logarithms can be used to measure the acidity or alkalinity of a solution. The pH of a solution is defined as the negative logarithm of the hydrogen ion concentration, or pH = -log10([H]). A solution with a pH of 7 is neutral, a solution with a pH less than 7 is acidic, and a solution with a pH greater than 7 is basic. For example, pure water has a pH of 7, lemon juice has a pH of about 2, and bleach has a pH of about 12.

• Sound intensity: Logarithms can be used to measure the loudness or intensity of a sound. The sound intensity level (SIL) of a sound is defined as 10 times the logarithm of the ratio of the sound intensity to a reference intensity, or SIL = 10log10(I/I0). The reference intensity I0 is usually taken as the threshold of human hearing, which is about 10 watts per square meter. The SIL is measured in decibels (dB). For example, a whisper has a SIL of about 20 dB, normal conversation has a SIL of about 60 dB, and a jet engine has a SIL of about 140 dB.

• Earthquake magnitude: Logarithms can be used to measure the strength or magnitude of an earthquake. The Richter scale is a logarithmic scale that assigns a number to an earthquake based on the amplitude of the seismic waves it produces. The Richter magnitude (M) of an earthquake is defined as M = log10(A/A0), where A is the amplitude of the seismic waves and A0 is a reference amplitude. The reference amplitude A0 is usually taken as one micrometer (one millionth of a meter). The Richter magnitude is measured in units called Richter units (RU). For example, a minor earthquake has a Richter magnitude of about 3 RU, a moderate earthquake has a Richter magnitude of about 5 RU, and a major earthquake has a Richter magnitude of about 7 RU.

## How to use a log table to find the logarithm of a number?

A log table is a table that lists the logarithms of numbers for a given base. Usually, the base is either 10 or e, and the numbers are between 1 and 10. A typical log table has four columns: the first column shows the number (or its first digit), the second column shows the characteristic (or the integer part) of the logarithm, the third column shows the mantissa (or the decimal part) of the logarithm, and the fourth column shows the number rounded to four decimal places. For example, here is part of a log table for base 10:

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Number Characteristic Mantissa Number --- --- --- --- ... ... ... ... 2 0 .3010 2.0000 2.1 0 .3222 2.1000 ... ... ... ... To use a log table to find the logarithm of a number, you need to follow these steps:

### Steps to use a log table

• Write the number in scientific notation, that is, as a product of a decimal number between 1 and 10 and a power of 10. For example, if the number is 234, write it as 2.34 x 10.

• Find the logarithm of the decimal number by looking up the first column of the log table and matching it with the first digit of the decimal number. Then, find the corresponding mantissa in the third column. For example, if the decimal number is 2.34, look up 2 in the first column and find the mantissa .3010 in the third column.

• Find the logarithm of the power of 10 by multiplying it by the base of the log table. For example, if the power of 10 is 2 and the base is 10, then the logarithm of the power of 10 is 2 x log10(10) = 2 x 1 = 2.

• Add the logarithm of the decimal number and the logarithm of the power of 10 to get the logarithm of the original number. For example, if the logarithm of the decimal number is .3010 and the logarithm of the power of 10 is 2, then the logarithm of the original number is .3010 + 2 = 2.3010.

• Round off the answer to four decimal places if necessary. For example, if the answer is 2.3010, then it can be written as 2.3010 or 2.301.

### Tips and tricks to use a log table efficiently

Here are some tips and tricks to use a log table efficiently:

• If the number has more than one digit after the decimal point, you can use interpolation to find a more accurate mantissa. For example, if the number is 2.34, you can find the mantissa for 2.3 and 2.4 in the log table, which are .3617 and .3802 respectively. Then, you can use this formula to find the mantissa for 2.34: mantissa for 2.34 = mantissa for 2.3 + (mantissa for 2.4 - mantissa for 2.3) x (0.04 / 0.1) = .3617 + (.3802 - .3617) x (0.04 / 0.1) = .3617 + .0074 = .3691.

• If the number has more than one digit before the decimal point, you can use antilogarithms to find a more accurate number. For example, if you have found that log10(x) = 3.4567, you can write x as x = y x 10, where y is a decimal number between 1 and 10. Then, you can find y by looking up the mantissa .4567 in the log table and finding the corresponding number in the fourth column, which is 2.8906. Therefore, x = y x 10 = 2.8906 x 10 = 2890.6.

• If you need to find the logarithm of a fraction or a decimal number less than one, you can use negative characteristics or negative exponents. For example, if you need to find log10(0.0234), you can write it as log10(23.4 x 10) = log10(23.4) + log10(10) = log10(23.4) - log10(1000) = log10(23.4) - 3 = -1 + log10(23.4). Then, you can use a log table to find log10(23.4), which is about .3699, and subtract it from -1 to get -1 - .3699 = -1.3699.

• If you need to find the logarithm of a product or a quotient of two numbers, you can use the properties of logarithms that state that logb(xy) = logb(x) + logb(y) and logb(x/y) = logb(x) - logb(y). For example, if you need to find log10(60), you can write it as log10(6 x 10) = log10(6) + log10(10) = .7782 + 1 = 1.7782. Similarly, if you need to find log10(0.06), you can write it as log10(6/100) = log10(6) - log10(100) = .7782 - 2 = -1.2218.

• If you need to find the logarithm of a number to a different base than the one given in the log table, you can use the change of base formula that states that loga(x) = logb(x) / logb(a). For example, if you need to find log2(8), but you only have a log table for base 10, you can write it as log2(8) = log10(8) / log10(2) = .9031 / .3010 = 3.

## Where to download a log table pdf for numbers 1 to 100?

If you want to download a log table pdf for numbers 1 to 100, you have several options. You can either search online for a reliable source, or you can create your own using a spreadsheet program or an online tool. Here are some benefits and sources of downloading a log table pdf:

• A log table pdf is portable and convenient. You can print it out and carry it with you wherever you go, or you can save it on your computer or mobile device and access it anytime.

• A log table pdf is accurate and precise. You can avoid errors and mistakes that may occur when using a calculator or doing mental calculations.

• A log table pdf is versatile and flexible. You can use it for any base and any number within the range of 1 to 100. You can also use it for different purposes and applications, such as homework, exams, projects, research, etc.

• A log table pdf is free and easy to use. You don't have to pay anything or register for anything to download a log table pdf. You just need to click on a link and save the file on your device. You also don't need any special skills or knowledge to use a log table pdf. You just need to follow the steps and tips mentioned above.

Here are some sources and links to download a log table pdf for numbers 1 to 100:

• [RapidTables.com]: This website provides an online tool that generates a log table for any base and any number. You can enter the base and the number in the input boxes, and click on the "Calculate" button. The tool will display the logarithm and the antilogarithm of the number for the given base. You can also see a log table for base 10, base e, and base 2 on the same page. You can download the pdf file from this link: [https://www.rapidtables.com/calc/math/Log_Calculator.html].

## Conclusion

In conclusion, a log table is a useful tool that can help you find the logarithm of any number without using a calculator. It can also help you solve various problems in mathematics and science that involve exponential growth or decay, compound interest, pH levels, sound intensity, earthquake magnitude, and more. To use a log table, you need to write the number in scientific notation, find the logarithm of the decimal number and the power of 10, and add them together. You can also use interpolation, antilogarithms, properties of logarithms, and change of base formula to improve your accuracy and efficiency. You can download a log table pdf for numbers 1 to 100 from various sources online, or you can create your own using a spreadsheet program or an online tool.

### Summary of the main points

• A log table is a table that lists the logarithms of numbers for a given base.

• A logarithm is the exponent or power that a base number must be raised to in order to get another number.

• A log table is useful because it helps you find the logarithm of any number without using a calculator.

• A log table also helps you solve various problems in mathematics and science that involve exponential growth or decay, compound interest, pH levels, sound intensity, earthquake magnitude, and more.

• To use a log table, you need to write the number in scientific notation, find the logarithm of the decimal number and the power of 10, and add them together.

• You can also use interpolation, antilogarithms, properties of logarithms, and change of base formula to improve your accuracy and efficiency.

• You can download a log table pdf for numbers 1 to 100 from various sources online, or you can create your own using a spreadsheet program or an online tool.

### Call to action and feedback

Now that you have learned how to use a log table, why don't you try it out for yourself? Download a log table pdf from one of the sources we provided, or create your own using a spreadsheet program or an online tool. Then, practice finding the logarithm of different numbers and solving different problems using a log table. You will be amazed by how much easier and faster it is than using a calculator or doing mental calculations.

Also, please let us know what you think about this article. Did you find it helpful and informative? Did you learn something new? Did you have any difficulties or challenges? Do you have any suggestions or recommendations? We would appreciate your honest feedback and constructive criticism. Your input will help us improve our content and provide better service to our readers.

Thank you for reading this article. We hope that you enjoyed it and learned something valuable from it. We look forward to hearing from you soon.

## FAQs

• Q: What is the difference between natural logarithm and common logarithm?

• A: Natural logarithm is the logarithm to the base e (approximately 2.718), which is denoted by ln(x) or loge(x). Common logarithm is the logarithm to the base 10, which is denoted by log(x) or log10(x). Natural logarithm is more commonly used in calculus and natural sciences, while common logarithm is more commonly used in engineering and computer science.

• Q: What is the inverse operation of logarithm?

• A: The inverse operation of logarithm is exponentiation. For example, if logb(x) = y, then b = x. Exponentiation means raising a base number to a power or exponent.

• Q: How do I find the logarithm of a negative number?

A: You cannot find the logarithm of a negative number using real