Vidaara.orgClass 9 · Mathematics
CodeVID-M09-21-LAW-01
Laws of Logarithms - Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$\log(mn)=$
- A.$\log m+\log n$
- B.$\log m-\log n$
- C.$\log m\cdot\log n$
- D.$\log(m+n)$
2.
$\log\dfrac{m}{n}=$
- A.$\log m+\log n$
- B.$\log m-\log n$
- C.$\dfrac{\log m}{\log n}$
- D.$\log(m-n)$
3.
$\log m^n=$
- A.$n\log m$
- B.$\log m+n$
- C.$m\log n$
- D.$(\log m)^n$
4.
$\log_a 1=$
- A.$0$
- B.$1$
- C.$a$
- D.undefined
5.
$\log 2+\log 5=$
- A.$\log 7$
- B.$\log 10$
- C.$\log 25$
- D.$\log 3$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Write $\log 2+\log 3$ as a single logarithm.
7.
Simplify $\log 8-\log 2$.
8.
Write $3\log 2$ as a single logarithm.
9.
Simplify $\log 2+\log 5$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
If $\log 2=0.301$, find $\log 8$.
11.
Simplify $\log 100-\log 10$.
12.
Express $\log 45$ using $\log 9$ and $\log 5$.
13.
Simplify $2\log 3+\log 2$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
If $\log 2=0.301$ and $\log 3=0.477$, find $\log 12$.
15.
Express $\log\dfrac{x^2 y}{z^3}$ as a sum/difference of logarithms.
Answer Key
Section A — Multiple Choice Questions
- (A) $\log m+\log n$
- (B) $\log m-\log n$
- (A) $n\log m$
- (A) $0$
- (B) $\log 10$
Section B — Short Answer (2 marks)
- $\log 6$.
- $\log 4$.
- $\log 8$.
- $\log 10$.
Section C — Short Answer (3 marks)
- $0.903$.
- $1$.
- $\log 9+\log 5$.
- $\log 18$.
Section D — Long Answer (5 marks)
- $1.079$.
- $2\log x+\log y-3\log z$.
Generated by Vidaara.org · Assignment VID-M09-21-LAW-01 · vidaara.org