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Vidaara.orgClass 9 · Mathematics
CodeVID-M9-21-CT
Logarithms — Full Chapter Test
Chapter: Logarithms
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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.
If $a^x=N$, then:
  • A.$\log_N a=x$
  • B.$\log_a N=x$
  • C.$\log_a x=N$
  • D.$\log_x N=a$
2.
$\log(mn)=$
  • A.$\log m+\log n$
  • B.$\log m-\log n$
  • C.$\log m\cdot\log n$
  • D.$\log(m+n)$
3.
The common logarithm has base:
  • A.$2$
  • B.$e$
  • C.$10$
  • D.$1$
4.
$\log_2 8=$
  • A.$2$
  • B.$3$
  • C.$4$
  • D.$8$
5.
$\log\dfrac{m}{n}=$
  • A.$\log m+\log n$
  • B.$\log m-\log n$
  • C.$\dfrac{\log m}{\log n}$
  • D.$\log(m-n)$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Write $2^3=8$ in logarithmic form.
7.
Write $\log 2+\log 3$ as a single logarithm.
8.
Evaluate $\log 100$.
9.
Write $\log_3 9=2$ in exponential form.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Evaluate $\log_2 32$.
11.
If $\log 2=0.301$, find $\log 8$.
12.
If $\log 2=0.301$, find $\log 200$.
13.
Evaluate $\log_3 81$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Convert to logarithmic form: $4^3=64$ and $10^{-2}=0.01$.
15.
If $\log 2=0.301$ and $\log 3=0.477$, find $\log 12$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\log_a N=x$
  2. (A) $\log m+\log n$
  3. (C) $10$
  4. (B) $3$
  5. (B) $\log m-\log n$
Section B — Short Answer (2 marks)
  1. $\log_2 8=3$.
  2. $\log 6$.
  3. $2$.
  4. $3^2=9$.
Section C — Short Answer (3 marks)
  1. $5$.
  2. $0.903$.
  3. $2.301$.
  4. $4$.
Section D — Long Answer (5 marks)
  1. $\log_4 64=3$ and $\log_{10} 0.01=-2$.
  2. $1.079$.
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