Unit 1: Number and Algebra
Topic 1.7: Laws of Exponents and Logarithms Questions
Practice 20 exam-style questions for IB Math AA SL Topic 1.7. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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Write down as a single power of .
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It is given that , where .
Show that .
Show that .
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Write down as a single logarithm.
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It is given that Σ from n = 3 to 10 of ln(n/(n + 1)) = ln(3/11).
Hence, write down the value of Σ from n = 3 to 2025 of ln(n/(n + 1)).
Hence, write down the value of Σ from n = 3 to 2025 of ln(n/(n + 1)).
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It is given that log₅ p = 2 + log₅ r, where p, r > 0.
Show that p = 25r.
Show that p = 25r.
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Express log 4 + log 25 as a single base-10 logarithm, and state its exact value.
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Write down the exact solution of .
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Express log 50 + log 20 as a single base-10 logarithm, and state its exact value.
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Given that (base 10), find log 16 in terms of p.
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It is given that Σ from n = 1 to 7 of ln(1 + 1/n) = ln 8.
Hence, write down the value of Σ from n = 1 to 2025 of ln(1 + 1/n).
Hence, write down the value of Σ from n = 1 to 2025 of ln(1 + 1/n).
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Simplify (a5/2 × a1/2) ÷ a, expressing your answer as a single power of a.
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It is given that for .
Write down the value of .
Write down the value of .
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It is given that for .
Write down the value of the sum when .
Write down the value of the sum when .
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Given that log 2 = p (base 10), find log 16 in terms of p.
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Write 2 log x + 3 log y as a single logarithm.
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It is given that log₂ p = 5 + log₂ r, where p, r > 0.
Show that p = 32r.
Show that p = 32r.
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Simplify , expressing your answer as a single power of a.
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