Logarithm Questions

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In CBSE board, chapters of logarithm are included in the syllabus of class 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 are 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 idea 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: The answer is 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: The answer is 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: The answer is 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 option (a) 512.

Students’ query 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!

FAQ (Frequently Asked Questions)

1. How to Solve Logarithm Basic Questions?

Ans. While the solution to be used will vary among logarithmic functions questions, the basic steps involve the following – 

  1. Determining the number of problems present in the logarithm 

  2. Apply relevant properties for simplification of the problem

  3. the problem has to be rewritten sans logarithms

  4. simplify problem further

  5. find the solution of x, and

  6. check the final solution. It must be noted for logs questions that logarithm of a negative number cannot be taken. 

2. What are the Different Properties to Keep in Mind for Solving Log Maths Questions?

Ans. There are four properties to be followed for solving logarithm questions. The properties are – (1) product property, (2) quotient property, (3) power property, and (4) change of base property. 

Product rule indicates that multiplying two or more logarithms with common bases becomes equal to the value arising out of separate logarithms. Quotient property lays down that two logarithms having same bases amounts to be equal to result generated from the difference in logarithms. Moreover, in case of change of base property, a given logarithm can be written with a new base. 

3. What are Logarithmic Functions?

Ans. The inverse of exponential functions is termed as logarithmic functions. The logarithmic function, y = logax corresponds to the exponential equation, x = ay. y = logax. However, this relation holds only under a specific condition. Only if – (1) x = ay, (2) a > 0, and (3) a≠1, will the relation be applicable. 

Having a clear idea about logarithmic functions is essential for solving even the basic log questions.