Unit 1: Number and Algebra
Topic 1.9: Log laws (HL only) Questions
Practice 11 exam-style questions for IB Math AI SL Topic 1.9. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
3Express2 marks
2026
Write log a + 2 log b − 3 log c as a single logarithm.
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2026
Solve log₃(2x − 1) = 4 for the number x of network nodes.
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2026
A population doubles every T years where 1.04ᵀ = 2. Then T is:
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2026
Given log 2 = 0.301 and log 3 = 0.477, find log 18 without a calculator.
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2026
A colony of bacteria grows so that after t hours it is multiplied by 1.15ᵗ. Find, to 3 s.f., the time for the colony to triple (1.15ᵗ = 3).
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2026
A 200 mg sample of an isotope decays as A = 200(0.5)t/8, with t in days. Find, to the nearest day, when 25 mg remains.
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2026
Sound intensity level is L = 10 log(I / I₀) decibels, where I₀ = 10⁻¹² W m⁻².
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