Logarithms
Practice Flashcards
What does log_a b mean?
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All Flashcards in Topic 1.5
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1.5.18 cards
What does log_a b mean?
The power you raise a to, to get b. a^x = b ⇔ x = log_a b. Example: log₂ 8 = 3 because 2³ = 8.
How do you convert a^x = b to log form?
Keep the base: log_a b = x. The log equals the exponent.
How do you convert log_a b = x to exponent form?
a^x = b. The log value x is the exponent of the base a.
What does log x (no base shown) mean?
log₁₀ x — base 10.
What does ln x mean?
log_e x — the natural logarithm, base e ≈ 2.718.
Why are logs and exponents inverses?
Taking log_a undoes raising a to a power: log_a(a^x) = x, and a^(log_a b) = b.
What is ln e?
1, because e¹ = e.
Write 5³ = 125 as a logarithm.
log₅ 125 = 3.
1.5.28 cards
How do you evaluate log_a b by hand?
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.
What is log_a 1, for any base a?
0 — because a⁰ = 1.
What is log_a a?
1 — because a¹ = a.
How do you evaluate log₂ (1/16)?
1/16 = 2⁻⁴, so log₂(1/16) = −4 (a reciprocal gives a negative power).
How do you evaluate log₉ 3?
3 = 9^(1/2), so log₉ 3 = ½ (a root gives a fractional power).
What is log_a (1/b) in terms of log_a b?
−log_a b — a reciprocal flips the sign.
How do you evaluate a logarithm on Paper 2?
Type log or ln on the GDC; for other bases use the change-of-base rule (topic 1.7).
Evaluate log₈ 2 by hand.
8^(1/3) = 2, so log₈ 2 = ⅓.
Topic 1.5 study notes
Full notes & explanations for Logarithms
Math AA SL exam skills
Paper structures, command terms & tips
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