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All 8 Flashcards — Logs as inverses
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Question
What does log_a b mean?
Answer
The power you raise a to, to get b. a^x = b ⇔ x = log_a b. Example: log₂ 8 = 3 because 2³ = 8.
Question
How do you convert a^x = b to log form?
Answer
Keep the base: log_a b = x. The log equals the exponent.
Question
How do you convert log_a b = x to exponent form?
Answer
a^x = b. The log value x is the exponent of the base a.
Question
What does log x (no base shown) mean?
Answer
log₁₀ x — base 10.
Question
What does ln x mean?
Answer
log_e x — the natural logarithm, base e ≈ 2.718.
Question
Why are logs and exponents inverses?
Answer
Taking log_a undoes raising a to a power: log_a(a^x) = x, and a^(log_a b) = b.
Question
What is ln e?
Answer
1, because e¹ = e.
Question
Write 5³ = 125 as a logarithm.
Answer
log₅ 125 = 3.
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Full study notes for Logs as inverses
Topic 1.5 hub
Logarithms
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Math AA SL exam skills
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