Logarithms (VCE SSCE General Mathematics): Flashcards

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Logarithms
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Definition of a logarithm

The power to which a number must be raised to get another number

Value of log100\log 100

22 (because 102=10010^2 = 100)

If log(x)=a\log(x) = a, then xx equals

10a10^a

Order of magnitude measures

Scale of quantities expressed as powers of 10

Increase by nn orders of magnitude means

Multiply by 10n10^n

Decrease by nn orders of magnitude means

Divide by 10n10^n

Method to find order of magnitude

Write in standard form; power of 10 is order of magnitude

Purpose of logarithmic transformation

Linearise curved data for easier analysis

When to use log10(x)\log_{10}(x) transformation

When data spans several orders of magnitude

Comparing quantities using logs: method

Subtract logs, then calculate 10difference10^{\text{difference}}

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