The Logarithm Questions are an important part of the** ****quantitative aptitude section**** **in the **upcoming government exams****.**

**Logarithm Questions **are asked in exams like:

Start your preparation by solving these questions. In this blog, we will review the fundamentals of **Logarithm Questions,** the types of questions asked in previous year exams and how to approach them. This will help you clear your basics and answer these **Logarithm Questions.**

Table of Contents

## What is Logarithm? What are Logarithm Problems?

“Lagorithm” is a term that is used to solve problems that are not solved just using the exponents. Writing the logarithm equation is another way to write the exponential equation.

It is an inverse form of exponents. There are 7 rules of logarithmic equations, such as:

- Product rule.
- Division rule.
- Power rule/Exponential Rule.
- Change of base rule.
- Base switch rule.
- Derivative of log.
- Integral of log.

### Formulae of Logarithm

The basic formulae for Logarithm are:

- logb(mn) = logb(m) + logb(n)
- logb(m/n) = logb (m) – logb (n)
- Logb (xy) = y logb(x)
- Logbm√n = logb n/m
- m logb(x) + n logb(y) = logb(xmyn)
- logb(m+n) = logb m + logb(1+nm)
- logb(m – n) = logb m + logb (1-n/m

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## 10 + Logarithm Questions and Answers

**Q.1. Find the value of log9 59049**

A. 9

B. 7

C. 5

D. 8

Answer: B

**Q.2. . If log 2 = 03.301 and log 3 = 0.4771, find the value of log3 725**

A. 19.46

B. 18.96

C. 21.54

D. 14.48

Answer: A

**Q.3. If x, y and z are the sides of a right-angled triangle, where ‘z’ is the hypotenuse, then find the value of (1/logx+zy) + (1/logx-zy)**

A. 1

B. 2

C. 3

D. 4

Answer: B

**Q.4. Find the value of log2 2 + log2 22 + log2 23 + …….. + log2 2n.**

A. n(n+1)/2

B. n+1

C. n

D. 2n

Answer: A

**Q.5. If log5 16, log5 (3x-4), log5 (3x+97/16) are in arithmetic progression, then x is**

A. 8

B. 1

C. 5

D. 3

Answer: B

**Q.6. If ‘x’ is an integer then solve (log2 x) 2 – log2 x4 – 32 = 0.**

A. 125

B. 256

C. 375

D. None of these

Answer: B

**Q.7. If log5y – logsub>5√y = 2 logy 5, then find the value of y.**

A. 25

B. 35

C. 10

D. 15

Answer: A

**Q8. If (1/4)log2x + 4log2y = 2 + log64-18 then**

A. y16 = 64/x2

B. x16 = 64/y

C. y16 = 8/x4

D. y16 = 64/x

Answer: D

**Q9. If log 2 = 0.301 and log 3 = 0.4771, find the number of digits in 4812.**

A. 19

B. 21

C. 20

D. 24

Answer: A

**Q10. If log3[log2 (x2 – 4x – 37)] = 1, where ‘x’ is a natural number, find the value of x.**

A. 9

B. 7

C. 10

D. 4

Answer: B

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## FAQs

**How to solve log problems with quantitative aptitude?**

There are many rules in the Logarithm equation to solve log problems in quantitative aptitude.

**How many rules are there in logarithmic equations?**

There are 7 rules in logarithmic equations such as:

Product rule.

Division rule.

Power rule/Exponential Rule.

Change of base rule.

Base switch rule.

Derivative of log.

Integral of log.

**What are the basic formulae for Logarithm problems?**

The basic formule for Logarithm problem is logb(mn) = logb(m) + logb(n).

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