Math 9th Chap 2 : Topic 3 - Maryam Publications

Math Chapter 2 : Topic 3

Common and Natural Logs

1 / 22

The base of a common logarithm is:

A) $2$

B) $1$

C) $10$

D) $e$

2 / 22

The base of a natural logarithm is:

A) $10$

B) $e$

C) $0$

D) $2$

3 / 22

Which notation represents natural logarithm?

A) $\log_{10}\ x$

B) $log\ x$

C) $ln\ x$

D) $lg\ x$

4 / 22

Which is the correct form of common logarithm?

A) $log\ x$

B) $\log_{10}\ x$

C) $ln\ x$

D) $loge\ x$

5 / 22

Which logarithm is most commonly used in calculators?

A) Common logarithm only

B) Both common and natural logarithm

C) Neither type

D) Natural logarithm only

6 / 22

The value of $\log_{10}\ 100$ is:

A) $100$

B) $2$

C) $10$

D) $1$

7 / 22

Which statement is correct?

A) log uses base $e$

B) $\ln$ uses base $e$

C) $\ln$ uses base $10$

D) log uses base $2$

8 / 22

The value of $e$ is approximately:

A) $3.14$

B) $2.71$

C) $10$

D) $2.14$

9 / 22

Which logarithm is called "Briggsian logarithm"?

A) Natural logarithm

B) Common logarithm

C) Binary logarithm

D) Exponential logarithm

10 / 22

Which expression is correct?

A) $log\ x = logₑ\ x$

B) $\log_{10}\ x \neq ln\ x$

C) $ln\ x = \log_{2}\ x$

D) $log\ x = ln\ x$

11 / 22

Which is true about $ln\ x$?

A) It has base $2$

B) It has no base

C) It has base $e$

D) It has base $10$

12 / 22

Which of the following is a natural logarithm?

A) $\log_{10}\ 100$

B) $log\ 100$

C) $\log_{2}\ 100$

D) $ln\ 100$

13 / 22

Common logarithm is also called:

A) Binary $\log$

B) Natural $\log$

C) Base $e$ $\log$

D) Base $10\ log$

14 / 22

Which is larger?

A) Both equal

B) Cannot compare

C) $ln\ 10$

D) $log\ 10$

15 / 22

Which logarithm is used in scientific growth and decay models?

A) Binary logarithm

B) Common logarithm

C) Natural logarithm

D) None

16 / 22

Which statement is correct?

A) $\ln$ is always greater than $\log$

B) log is always greater than $\ln$

C) log and $\ln$ are identical

D) They differ by base

17 / 22

Which of the following equals $1$?

A) $ln\ 10$

B) ${ln\ e}^{2}$

C) $\log_{10}\ 10$

D) $\log_{10}\ 100$

18 / 22

Which is true about natural logarithm?

A) Used only in geometry

B) Not used in science

C) Used only in finance

D) Used in exponential growth

19 / 22

Which is correct relation?

A) $log\ x = ln\ 10$

B) $ln\ x = \log_{e}\ x$

C) $log\ x = \log_{2}\ x$

D) $ln\ x = \log_{10}\ x$

20 / 22

Which pair is correctly matched?

A) Both have same base

B) $log\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightarrow \ \ \ base\ 10\ $, $ln\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightarrow \ \ \ base\ e$

C) $log\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightarrow \ \ \ base\ 2\ $, $ln\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightarrow \ \ \ base\ 10$

D) $log\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightarrow \ \ \ base\ e\ $, $ln\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightarrow \ \ \ base\ 10$

21 / 22

Which is NOT a logarithm type?

A) Natural logarithm

B) Binary logarithm

C) Common logarithm

D) Scientific logarithm

22 / 22

Which logarithm is most useful in calculus?

A) Common logarithm

B) Natural logarithm

C) Base $2$ logarithm

D) Base $10$ logarithm

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