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Log Table from 1 to 100: PDF Format and Free Download


Log Table PDF Download 1 to 100




Do you need to find the logarithm of a number quickly and accurately? Do you want to learn how to use a log table to solve complex problems in mathematics and science? Do you want to download a log table pdf for numbers 1 to 100 for free? If you answered yes to any of these questions, then this article is for you. In this article, you will learn what a log table is, why it is useful, how to use it, and where to download it. By the end of this article, you will be able to use a log table with confidence and ease.


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.




log table pdf download 1 to 100



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:


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  • 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:


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 1


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