Logarithms quiz
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What do logarithms turn multiplication into?
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More questions about Logarithms
These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.
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What is $\log_{10} 0.01$?
Answer: −2
Why: Every number between 0 and 1 has a negative log in base 10, because it takes a negative power: $10^{-2} = \frac{1}{100}$.
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How few yes/no questions always pin down a number up to a million?
Answer: 20
Why: Each answer halves the range, and $2^{20}$, which is 1,048,576, is the first power of two above a million.
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Who invented logarithms independently of Napier?
Answer: Jost Bürgi
Why: A Swiss clockmaker, Bürgi published his tables only in 1620, six years after Napier's book appeared.
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How many times must you double 1 to reach 1,024?
Answer: 10
Why: Because $2^{10}$ is just over 1,000, 20 doublings pass a million and 30 pass a billion.
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Across which line is $\ln x$ the mirror image of $e^x$?
Answer: $y = x$
Why: Inverse functions swap coordinates, so the point (0, 1) on $e^x$ becomes (1, 0) on $\ln x$, its mirror image across $y = x$.
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How often is 1 the first digit in data such as river lengths?
Answer: About 30%
Why: Benford's law gives digit d a share of $\log_{10}(1 + \frac{1}{d})$, so 1 leads 30.1% of the time and 9 only 4.6%.
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