Logarithms (laws of logarithms, common logarithms, applications) — KCSE Mathematics

KCSE Mathematics · 104 practice questions · 4 syllabus objectives

35 easy34 medium35 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Define a logarithm and convert between index form (aˣ = N) and logarithmic form (log_a N = x)

Apply the laws of logarithms (log AB = log A + log B, log A/B = log A – log B, log Aⁿ = n log A) to simplify and evaluate expressions

Use logarithm tables (or a calculator) to multiply, divide, find powers and roots of numbers; solve equations of the form aˣ = b

Logarithms (laws of logarithms, common logarithms, applications)

Sample Questions

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1
easySHORT ANSWER5 marks

In the context of mathematical analysis, the manipulation and application of logarithmic expressions play a crucial role in solving various equations. Consider the following problems that involve simplifying logarithmic terms, deriving values, and evaluating specific logarithmic expressions under defined constraints. (a) Simplify: log 18 + log 6 − log 3. (2 marks) (b) Given log 7 = 0.699, find log 7^4. (1 mark) (c) Evaluate: log₁₀(0.01) + log₁₀(10). (2 marks)

View Marking Scheme
Part (a) — 2 marks
log(18×6/3) (1 mk)
Simplified value (1 mk)
Part (b) — 1 mark
log7^4=4×0.699 (1 mk)
Part (c) — 2 marks
log(0.01×10) (1 mk)
Correct value (1 mk)
2
easySHORT ANSWER3 marks

Explain how to use logarithm tables to find the product of 50 and 20. (3 marks)

View Marking Scheme
Part (a) — 3 marks
Find log₁₀(50) from logarithm tables (1 mk)
Find log₁₀(20) from logarithm tables (1 mk)
Add the two logarithmic values and find the antilogarithm of the sum (1 mk)
3
easySHORT ANSWER2 marks

Name the value of x in the equation 10^x = 1000 using logarithms. (2 marks)

View Marking Scheme
Part (a) — 2 marks
x = log₁₀(1000) (1 mk)
x = 3 (1 mk)
4

Name two properties of logarithms that can be used to simplify the expression log₁₀(50) + log₁₀(2). (2 marks)

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