Calculus with Other Bases (HSC SSCE Mathematics Advanced): Flashcards

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Calculus with Other Bases
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Change-of-base formula for logax\log_a x

logax=logexlogea\log_a x = \frac{\log_e x}{\log_e a}

Derivative of logax\log_a x

1xlogea\frac{1}{x \log_e a}

Express aa as power of ee

a=elogeaa = e^{\log_e a}

Express axa^x in base ee

ax=exlogeaa^x = e^{x \log_e a}

Derivative of axa^x

axlogeaa^x \log_e a

Integral of axa^x

axlogea+C\frac{a^x}{\log_e a} + C

Gradient at x-intercept of y=logexy = \log_e x

11

Gradient at x-intercept of y=logaxy = \log_a x

1logea\frac{1}{\log_e a}

When diff./int. axa^x, multiply/divide by what constant?

logea\log_e a

Restriction on base aa

Positive and not equal to 11

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