Log Table PDF

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Log Table PDF Details
Log Table
PDF Name Log Table PDF
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Log Table

Here in this post, we are presenting Log Table PDF.  Those students who are searching Log Table Elements PDF for educational purposes can find it here with one click. The logarithmic table plays a very important role in mathematics. log table pdf is used to find the value of the logarithmic function. A logarithm table is a list of the mantissa (decimal part) of the exponents that make up base 10 numbers. They mean that the logarithm (the exponent) which works on base 10 to make 120, is 2.07918.

So don’t get confused and find the root and log off any numerical digit to get the table to calculate its value. The logarithm of a given number x is the exponent to which another fixed number, base b, must be raised to produce that number x.

Log Table PDF – Highlights

Log tables are used to perform large calculations (multiplication, division, square, and root) without using a calculator. The logarithm of a number for a given base is the exponent by which that base must be raised to give the original number. For example, if log₂16 = x then 2x = 16 and x = 4 satisfies this equation. So log₂ 16 = 4. But what about log₂ 15? If we assume log₂ 15 = x, we get 2x = 15 and we cannot find the value of x manually here. Logarithm table helps us to find the value of logarithm 15.

In this article, we will learn how to use the logarithm table. Let us see how to find the logarithm of a number using log table and how log is used in doing calculations along with many other examples.

Characteristic (Positive and Negative)

Number Scientific Notation Characteristic of Log of Number
23.78 2.378 × 101 1
4.572 4.572 × 100 0
552 5.52 × 102 2
0.172 1.72 × 10-1 -1
0.0172 1.72 × 10-2 -2

Thus, the logarithm characteristic of a number does not depend on the log table. Here are some useful tips for computing the logarithm of a number without actually converting it to scientific notation.

  • If the number is greater than 1, use the formula: attribute = number of digits to the left of the decimal point -1.
  • If the number is less than 1, use the formula: attribute = – (decimal point + 1 immediately after the number of zeros)

Let us look at the same example (as in the previous table) and calculate their characteristics using these tips.

If Number > 1
Number Number of digits on the left side of the decimal point Characteristic
23.78 2 2 – 1 = 1
4.572 1 1 – 1 = 0
552 (552.0) 3 3 – 1 = 2
If Number < 1
Number Number of zeros that immediately followed the decimal point Characteristic
0.172 0 – (0 + 1) = -1
0.0172 1 – (1 + 1) = -2

How to Use Logarithm Table?

The logarithm of any number has two parts: the characteristic and the mantissa. These two parts are always separated by a decimal point. For example, log 23.78 = 1.3762, and here, 1 is called the attribute, and 3762 is called the mantissa. That is, in the logarithm of a number:

  • The integer part (which is to the left of the decimal point) is called the characteristic;
  • The decimal (or) fractional part (located to the right of the decimal point) is called the mantissa.

Logarithm Table Characteristic (Positive and Negative)

The characteristic of the logarithm of a number is the exponent of 10 in its scientific notation. So the characteristic can be either positive or negative. Here are some examples to understand what is characteristic.

Number Scientific Notation Characteristic of Log of Number
23.78 2.378 × 101 1
4.572 4.572 × 100 0
552 5.52 × 102 2
0.172 1.72 × 10-1 -1
0.0172 1.72 × 10-2 -2

The logarithmic function is defined as an inverse function to exponentiation. The logarithmic function is stated as follows

For x, a > 0, and a≠1,

y= logx, if x = ay

Then the logarithmic function is written as:

f(x) = logx

The most common bases used in logarithmic functions are base e and base 10. The log function with base 10 is called the common logarithmic function and it is denoted by log10 or simply log.

f(x) = log10

The log function to the base e is called the natural logarithmic function and it is denoted by loge.

f(x) = loge x

To find the logarithm of a number, we can use the logarithm table instead of using a mere calculation. Before finding the logarithm of a number, we should know about the characteristic part and mantissa part of a given number

  • Characteristic Part – The whole part of a number is called the characteristic part. The characteristic of any number greater than one is positive, and if it is one less than the number of digits to the left of the decimal point in a given number. If the number is less than one, the characteristic is negative and is one more than the number of zeros to the right of the decimal point.
  • Mantissa Part – The decimal part of the logarithm number is said to be the mantissa part and it should always be a positive value. If the mantissa part is in a negative value, then convert it into a positive value.

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