Logarithm Questions

In the CBSE board, chapters of Logarithm are included in the syllabus of classes 9, 10, and 11. Students of class 9 will be introduced to Logarithm questions and answers for the very first time. Hence, the thorough practice of Logarithm problems and answers is the need of the hour. 

However, before proceeding with the chapter on Logarithm, students should be absolutely clear on the basic concepts. It is only then that solving difficult Logarithm questions would become considerably easier. 

Questions Based on Logarithm

Here are some of the Logarithm questions that would impart some ideas to students.  

Question 1: Find Out the Incorrect Statement from Below -

(a) log (1 + 2 + 3) = log 1 + log 2 + log 3

(b) log (2 + 3) = log (2 x 3)

(c) log10 10 = 1

(d) log10 1 = 0

Solution: The answer is option (b) log (2 + 3) = log (2 x 3). 

Question 2: What is the Value of log5512, when log 2 = 0.3010 and log 3 = 0.4771?

(a) 3.912

(b) 3.876

(c) 2.967

(d) 2.870

Solution: The answer is option (b) 3.876.

Question 3: Find the Value of log 9, When log 27 Amounts to 1.431.

(a) 0.954

(b) 0.945

(c) 0.958

(d) 0.934

Solution: An answer is an option (a) 0.954.

Question 4: What is the Value of log2 10, When log10 2 = 0.3010?

(a) 1000/301

(b) 699/301

(c) 0.6990

(d) 0.3010

Solution: An answer is an option (a) 1000/301.

Question 5: What is the Value of log10 80, When log10 2 = 0.3010?

(a) 3.9030

(b) 1.9030

(c) 1.6020

(d) None of the above option 

Solution: An answer is an option (b) 1.9030. 

Question 6: How Many Digits are there in 264 When log 2 = 0.30103?

(a) 21

(b) 20

(c) 18

(d) 19

Solution: The answer is option (b) 20.

Question 7: Which of the Following is True, if ax = by?

(a) log a/log b = x/y

(b) log a/b = x/y

(c) log a/log b = y/x

(d) None of the above option 

Solution: The answer is option (c) log a/log b = y/x. 

Question 8: What is the Value of log2 16?

(a) 8

(b) 4

(c) 1/8

(d) 16

Solution: The answer is (b) 4.

Question 9: Find the Value of y, if logx y = 100 and log2 x = 10.

(a) 21000

(b) 210

(c) 2100

(d) 210000

Solution: The answer is option (a) 21000.

Question 10: Find the Value of log10 (0.0001).

(a) – 1/4

(b) 1/4

(c) 4

(d) - 4

Solution: The answer is option (d) – 4.

Question 11: What is the Value of x When log2 [log3 (log2x)] = 1?

(a) 512

(b) 12

(c) 0

(d) 128

Solution: The answer is an option (a) 512.

Students’ queries simply and straightforward on Logarithm questions can be clarified in Vedantu’s online classes. You also have the option of downloading PDF materials from the official website. Download the app today!

Logarithm problems and answers are offered for students to solve to fully grasp the subject. These questions are based on the Logarithm chapter in the syllabus for Classes 9, 10, and 11. Practicing these problems will not only help students perform well in academic examinations, but will also allow them to compete in state or national level competitions such as Maths Olympiad.

The Logarithmic function is the exponential function's inverse. It is defined as follows:

If and only if x=ay, then y=logax; for x>0, a>0, and a1.

Logarithms are another way of expressing exponents in Mathematics. A number's Logarithm with a base equals another number. Exponentiation is the inverse function of Logarithm. For instance, if 102 = 100, log10 100 = 2.

As a result, we may deduce that

bn = x or log b x = n

Where b is the Logarithmic function's base.

This may be translated as "the Logarithm of x to the base b equals n."

In this post, we will cover the concept of Logarithms, the two types of Logarithms (common Logarithm and Natural Logarithm), and several Logarithmic characteristics with numerous solved cases.

History

In the 17th century, John Napier invented the notion of Logarithms. Later, it was utilized by many scientists, navigators, engineers, and others to accomplish numerous computations, which simplified it. Logarithms, in a nutshell, are the inverse process of exponentiation.

What Exactly are Logarithms?

A Logarithm is defined as the number of powers to which a number must be increased to obtain some other numbers. It is the simplest way to express enormous numbers. A Logarithm has many key features that demonstrate that Logarithm multiplication and division may also be stated in the form of Logarithm addition and subtraction.

"The exponent by which b must be raised to give an is the Logarithm of a positive real number a concerning a  base b, a positive real number not equal to 1[nb 1]."

in other words, by=a ⇔logba=y

Where,

The letters "a" and "b" represent two positive real numbers.

y is a valid number.

"a" is the argument, which is located within the log, and "b" is the base, which is located at the bottom of the log.

In other terms, the Logarithm answers the question, "How many times is a number multiplied to get the other number?"

For example, how many threes must be multiplied to reach the answer 27?

When we multiply 3 by 3, we get the answer 27.

As a result, the Logarithm is 3.

The Logarithmic form is as follows:

Log3 (27) = 3..... (1)

As a result, the base 3 Logarithm of 27 is three.

The Logarithm form shown above can alternatively be expressed as:

3x3x3 = 27

33 = 27..... (2)

As a result, equations (1) and (2) have the same meaning.

Types of Logarithms

In most circumstances, we are dealing with two forms of Logarithms, notably

• Common Logarithms

• Natural Logarithms

Common Logarithms

The base 10 Logarithms are another name for the common Logarithm. It is denoted by log10 or just log. The common Logarithm of 1000, for example, is expressed as a log (1000). The common Logarithm specifies how many times the number 10 must be multiplied to obtain the appropriate result.

For instance, log (100) = 2

When we multiply 10 by itself twice, we obtain the number 100.

Natural Logarithm

The base e Logarithm is another name for the natural Logarithm. The natural Logarithm is denoted by the symbols ln or loge. In this case, "e" stands for Euler's constant, which is approximately equal to 2.71828. The natural Logarithm of 78, for example, is represented as ln 78. The natural Logarithm specifies how many times "e" must be multiplied to obtain the appropriate result.

For instance, ln (78) = 4.357.

As a result, the base e Logarithm of 78 is 4.357.

Logarithm Properties and Rules

Logarithmic operations can be conducted according to specific rules. These rules are known as:

• Product rule

• Division rule

• Power rule/Exponential Rule

• Change of base rule

• Base switch rule

• Derivative of log

• Integral of log