Logarithms (laws of logarithms, common logarithms, applications) — KCSE Mathematics
KCSE Mathematics · 104 practice questions · 4 syllabus objectives
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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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)
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Explain how to use logarithm tables to find the product of 50 and 20. (3 marks)
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Name the value of x in the equation 10^x = 1000 using logarithms. (2 marks)
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