Logarithms (VCE SSCE Mathematical Methods): Flashcards

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Logarithms
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Express ax=ya^x = y in logarithmic form

log⁡ay=x\log_a y = x

Domain of log⁡ay\log_a y

y>0y > 0 (positive values only)

Notation for log⁡ex\log_e x

ln⁡x\ln x

Base of common logarithm

1010

log⁡a(mn)\log_a(mn)

log⁡am+log⁡an\log_a m + \log_a n

log⁡a(mn)\log_a\left(\frac{m}{n}\right)

log⁡am−log⁡an\log_a m - \log_a n

log⁡a(mp)\log_a(m^p)

plog⁡amp \log_a m

Value of log⁡a1\log_a 1

00

Value of log⁡aa\log_a a

11

Simplify log⁡a(ax)\log_a(a^x)

xx

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