Calculus & Differential Equations (Leaving Cert Applied Maths): Quizzes

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Logarithms
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What operation do logarithms reverse?

Raising numbers to powers

If 25=322^5 = 32, how is this written using logarithms?

log⁡232=5\log_2 32 = 5

In log⁡an=m\log_a n = m, what is aa called?

The base

What does log⁡a(xy)\log_a(xy) equal?

log⁡ax+log⁡ay\log_a x + \log_a y

What does log⁡a(xy)\log_a(\frac{x}{y}) simplify to?

log⁡ax−log⁡ay\log_a x - \log_a y

How is log⁡a(xp)\log_a(x^p) rewritten using the power rule?

plog⁡axp \log_a x

What does log⁡a(ax)\log_a(a^x) equal?

xx

If log⁡ab=log⁡ac\log_a b = \log_a c, what can you conclude?

b=cb = c

For what type of values are logarithms defined?

Positive arguments only

What does ln⁡5\ln 5 mean?

log⁡e5\log_e 5

What values can the base aa in log⁡an\log_a n take?

Positive, not equal to 1

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