IOQM · Mathematics · Basic Preliminaries
Logarithms
Log laws, change of base, log inequalities — pre-calculus level.
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- Previous papers: 10 official question papers from HBCSE-TIFR (Mathematical Olympiad Cell) — 2025, 2024, 2022-23, 2021-22 and 1 earlier year.
- Practice: 4 answer-checked practice questions on Logarithms for IOQM — practise them.
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Practice this topic
Take a full mock →Q1 · Logarithms · EASY
If log₁₀(x) = 3, what is the value of x?
Q2 · Logarithms · MEDIUM
If log₂(x) + log₂(x − 3) = 2, what is the value of x?
Q3 · Logarithms · MEDIUM
If log_a(b) = 2 and log_b(c) = 3, what is log_a(c)?
Q4 · Logarithms · HARD
If log₃(log₄(log₅(x))) = 0, what is the value of x?