Using a Logarithmic (Base 10) Scale to Display Data (VCE SSCE General Mathematics): Flashcards

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Using a Logarithmic (Base 10) Scale to Display Data
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Purpose of logarithmic scales

Display data spanning several orders of magnitude

What log scale does to small vs large values

Spreads out smaller values, compresses larger values

Logarithm to base 10 definition

Exponent when number is expressed as power of 10

If log10(x)=b\log_{10}(x) = b, then...

10b=x10^b = x

log10(100)\log_{10}(100) equals

22 (because 102=10010^2 = 100)

Log sign for numbers greater than 1

Positive (greater than zero)

Log sign for numbers between 0 and 1

Negative

Logarithm of zero

Undefined (cannot take log of zero or negative numbers)

Effect of log transformation on skewed distribution

Changes highly skewed to approximately symmetric

Equal distances on log scale represent

Equal ratios, not equal differences

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