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Flip to reveal answersState the three log laws (same base a).
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All 8 Flashcards — Log laws
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Question
State the three log laws (same base a).
Answer
log(xy) = log x + log y; log(x/y) = log x − log y; log(xⁿ) = n log x.
Question
What does logₐ x = y mean in index form?
Answer
aʸ = x — 'the power of a that gives x'. Logs and powers are inverse operations.
Question
What is the change-of-base rule?
Answer
logₐ x = log x / log a = ln x / ln a (number on top, old base on the bottom).
Question
How do you solve aˣ = b for x?
Answer
Take logs both sides: x log a = log b, so x = log b / log a (the doubling-time / half-life move).
Question
How do you solve logₐ N = k?
Answer
Rewrite in index form: N = aᵏ. Then check the inside of the log is positive.
Question
What are logₐ 1 and logₐ a?
Answer
logₐ 1 = 0 (a⁰ = 1) and logₐ a = 1 (a¹ = a).
Question
Why must you check the domain after solving a log equation?
Answer
Logs are only defined for positive inputs; reject any solution that makes the inside ≤ 0, even if the algebra allows it.
Question
Write 2 log P + log Q − log 5 as one logarithm.
Answer
log(P²Q / 5) — power law first, then product (add) and quotient (subtract).
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Topic 1.9 hub
Log laws (HL only)
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