Logarithms (HSC SSCE Mathematics Advanced): Flashcards

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Logarithms
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loga(x)=y\log_a(x) = y meaning

Exponent yy where ay=xa^y = x

Base constraint for logarithms

a>0a > 0 and a1a \neq 1

Argument constraint in loga(x)\log_a(x)

x>0x > 0 (must be positive)

Common logarithm notation & base

log(x)\log(x), base 10

Natural logarithm notation & base

ln(x)\ln(x), base ee

Logarithms & exponentials relationship

Inverse operations (undo each other)

102=10010^2 = 100 in logarithmic form

log(100)=2\log(100) = 2

log2(8)=3\log_2(8) = 3 in exponential form

23=82^3 = 8

Approximate value of Euler's constant ee

e2.71828e \approx 2.71828

Inverse property: eln(x)=?e^{\ln(x)} = ?

xx (where x>0x > 0)

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