The Laws of Logs (Leaving Cert Mathematics): Quizzes

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The Laws of Logs
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12 questions from this quiz

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Logarithms are the inverse of what mathematical operation?

Exponentials

What restriction applies to the base aa in log⁡a(x)\log_a(x)?

a>0a > 0 and a≠1a \neq 1

What restriction applies to the argument xx in log⁡a(x)\log_a(x)?

x>0x > 0

What does log⁡a(xy)\log_a(xy) equal according to the Product Rule?

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

What does log⁡a(xy)\log_a\left(\frac{x}{y}\right) equal according to the Quotient Rule?

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

What does log⁡a(xq)\log_a(x^q) equal according to the Power Rule?

q⋅log⁡a(x)q \cdot \log_a(x)

What does log⁡a(1x)\log_a\left(\frac{1}{x}\right) equal?

−log⁡a(x)-\log_a(x)

What is the value of log⁡a(1)\log_a(1) for any valid base aa?

00

What does alog⁡a(x)a^{\log_a(x)} equal?

xx

What does log⁡a(ax)\log_a(a^x) equal according to the Inverse Property?

xx

Evaluate log⁡b(1b2)\log_b\left(\frac{1}{b^2}\right).

−2-2

What question do logarithms answer?

To what power must base aa be raised to get xx?

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