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Flip to reveal answersHow do you evaluate log_a b by hand?
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All 8 Flashcards — Evaluating logs
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Question
How do you evaluate log_a b by hand?
Answer
Ask 'a to what power gives b?' — write b as a power of a; the exponent is the answer. E.g. log₃ 81 = 4 since 3⁴ = 81.
Question
What is log_a 1, for any base a?
Answer
0 — because a⁰ = 1.
Question
What is log_a a?
Answer
1 — because a¹ = a.
Question
How do you evaluate log₂ (1/16)?
Answer
1/16 = 2⁻⁴, so log₂(1/16) = −4 (a reciprocal gives a negative power).
Question
How do you evaluate log₉ 3?
Answer
3 = 9^(1/2), so log₉ 3 = ½ (a root gives a fractional power).
Question
What is log_a (1/b) in terms of log_a b?
Answer
−log_a b — a reciprocal flips the sign.
Question
How do you evaluate a logarithm on Paper 2?
Answer
Type log or ln on the GDC; for other bases use the change-of-base rule (topic 1.7).
Question
Evaluate log₈ 2 by hand.
Answer
8^(1/3) = 2, so log₈ 2 = ⅓.
Read the notes
Full study notes for Evaluating logs
Topic 1.5 hub
Logarithms
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Math AA SL exam skills
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