Logarithmic Functions (AQA A-Level Mathematics): Quizzes

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Logarithmic Functions
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What does log⁡5(125)\log_5(125) ask?

What power gives 125125 from 55?

What is log⁡2(8)\log_2(8)?

33

If no base is written for a logarithm, what base is assumed?

1010

What is the alternative notation for log⁡e(y)\log_e(y)?

ln⁡(y)\ln(y)

What does log⁡(y)\log(y) represent when written without a base?

log⁡10(y)\log_{10}(y)

Using the product rule, log⁡a(xy)\log_a(xy) equals:

log⁡a(x)+log⁡a(y)\log_a(x) + \log_a(y)

Using the quotient rule, log⁡a(xy)\log_a\left(\frac{x}{y}\right) equals:

log⁡a(x)−log⁡a(y)\log_a(x) - \log_a(y)

Using the power rule, log⁡a(xn)\log_a(x^n) equals:

nlog⁡a(x)n \log_a(x)

The change of base formula states log⁡a(x)\log_a(x) equals:

log⁡b(x)log⁡b(a)\frac{\log_b(x)}{\log_b(a)}

If log⁡a(y)=x\log_a(y) = x, then in exponential form:

ax=ya^x = y

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