[Maths Class Notes] on Log base 2 Pdf for Exam

• A Logarithmic Function is a function that is the inverse of an exponential function.

• The purpose of the logarithm is to tell us about the exponent.

• Logarithmic Functions are used to explore the properties of exponential functions and are used to solve various exponential equations.

Log base 2 is an inverse representation of the power of 2. For example, n = bx  here, n is a real positive number. And x is the exponent number. Then, the log base format of this is Logb n = x. 

 

 

What is Log Base 2 or Binary Logarithm?

• Log base 2 is also known as binary logarithm.

• It is denoted as (log2n).

• Log base 2 or binary logarithm is the logarithm to the base 2.

• It is the inverse function for the power of two functions.

• Binary logarithm is the power to which the number 2 must be raised in order to obtain the value of n.

• Here’s the general form.

 

[{mathbf{x}}{text{ }} = {text{ }}{mathbf{lo}}{{mathbf{g}}_{mathbf{2}}}{mathbf{n}};;;boxed{} –  –  –  –  –  –  –  –  – boxed{}{{mathbf{2}}^{mathbf{x}}} = {text{ }}{mathbf{n}}]

 

 

Graph for Log Base 2

Properties of Log Base 2

There are a few properties of logarithm functions with base 2. They are listed in the table below.

Since we are discussing log base2, we will consider the base to be 2 here.

 

Basic Log Rules

 

Here are a Few Examples That show How the above Basic Rules work

Example 1 –

Log 40, which can be further written as,

Log (20× 2)

by-product rule 

= log 20 + log 2

which is equal to log 40

 

Example 2 – 

Find the value of log4(4)?

 logb(b) = 1, by identity rule

Therefore, log4(4) = 1.

 

The Formula for Change of Base

The logarithm can be in the form of log base e or log base 10 or any other bases. Here’s the general formula for change of base –

[{mathbf{Lo}}{{mathbf{g}}_{mathbf{b}}};{mathbf{x}}{text{ }} = {text{ }}frac{{{mathbf{Lo}}{{mathbf{g}}_{mathbf{a}}};{mathbf{x}}}}{{{mathbf{Lo}}{{mathbf{g}}_{mathbf{a}}};{mathbf{b}}}};]

To find the value of log base 2, we first need to convert it into log base 10 which is also known as a common logarithm.

[Log{text{ }}base{text{ }}2{text{ }}of{text{ }}x = frac{{lnleft( x right)}}{{lnleft( 2 right)}}]

 

Now You might be wondering What Common Logarithmic Function is?

• Common Logarithmic Function or Common logarithm is the logarithm with base equal to 10.

• It is also known as the decimal logarithm because of its base.

• The common logarithm of x is denoted as log x.

• Example: log 100 = 2 (Since 102= 100).

 

How to Calculate Log Base 2?

This is how to find log base 2 –

 

Log Rule – 

[log_{b}(x) = y]

[b^{y} = x]

 

•  Suppose we have a question, log216 = x

• Using the log rule,

• 2x= 16

• We know that 16 in powers of 2 can be written as (2×2×2×2 =16) ,2x=24

• Therefore, x is equal to 4.

 

Questions to be Solved –

Question 1) Calculate the value of log base 2 of 64.

Solution) Here, 

X= 64

Using the formula,

[Log{text{ }}base{text{ }}2{text{ }}of{text{ }}X = frac{{lnleft( {64} right)}}{{lnleft( 2 right)}} = 6].

Log base 2 of 64 =[frac{{lnleft( {64} right)}}{{lnleft( 2 right)}} = 6].

Therefore, Log base 2 of 64 = 6

 

Question 2) Find the value of log2(2).

Solution) To find the value of log2(2) we will use the basic identity rule,

[lo{g_b}left( b right){text{ }} = {text{ }}1,].

Therefore, log2(2) = 1.

 

Question 3) What is the value of log 2 base 10?

Solution) The value of log 2 base 10 can be calculated by the rule,

[Lo{g_a}left( b right){text{ }} = frac{{log b}}{{log a}}].

[Lo{g_{10}}left( 2 right){text{ }} = frac{{log 2}}{{log 10}}; = {text{ }}0.3010].

Therefore, the value of log 2 base 10 = 0.3010.

 

Question 4) What is the value of log 10 base 2?

Solution) The value of log 10 base 2 can be calculated by the rule,

[Lo{g_b}left( a right){text{ }} = frac{{log b}}{{log a}}].

[Lo{g_2}left( {10} right){text{ }} = frac{{log 10}}{{log 2}}; = {text{ 3}}{text{.3 = 2}}].

Therefore, the value of log 10 base 2 = 3.32.

 

Uses of Logarithms in Everyday Life

• Earthquakes are recorded on seismographs and the amplitude is recorded on the Ritcher scale. Logarithmic values are used to comprehend these values

• It is also used in determining the pH value of any substance

• logarithms are used in measuring the sound intensity. Generally, sound intensity is measured by loudness which in turn is measured using logarithms

• They are also used in measuring complex values.

 

How to improve Scores in the Logarithm Chapter

Logarithm is just the opposite of expressing a number to the power of a digit. Many students face difficulty with this subject as they have to think and solve the problems in reverse. Following are some tips to improve your scores in logarithms:

• Understand that logarithm is an inverse expression of powers or exponents. All you have to do is solve them inversely

• Byheart learn all the laws of the logarithm and know what would be the end result for a particular problem if they solve it with the help of a formula

• Understanding the end result can be done by understanding the formula you apply to solve a problem. When you apply a formula that has the answer, you will get to know the end result

• Practice as many problems as you can with different logarithmic values

• Refer to the previous year questions to know the exam pattern, types of questions asked in the exam and assess the depth of the questions asked by the examiner.

• Any doubts can be clarified with your subject teacher or can be clarified from an online learning website like .