Change of Base Law (Leaving Cert Mathematics): Quizzes

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Change of Base Law
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Why is the Change of Base Law useful for calculator work?

Calculators only support log⁡\log & ln⁡\ln

What is the Change of Base Law formula?

log⁡bx=log⁡axlog⁡ab\log_bx=\frac{\log_ax}{\log_ab}

In the formula log⁡bx=log⁡axlog⁡ab\log_bx=\frac{\log_ax}{\log_ab}, what does bb represent?

The original base

In the formula log⁡bx=log⁡axlog⁡ab\log_bx=\frac{\log_ax}{\log_ab}, what does aa represent?

The new base

In log⁡bx=log⁡axlog⁡ab\log_bx=\frac{\log_ax}{\log_ab}, what does xx represent?

The argument of the logarithm

What is the theoretical basis for the Change of Base Law?

The definition of logarithms

Which bases are typically chosen when applying the Change of Base Law?

a=10a=10 or a=ea=e

When logs have different bases, which base is typically better to change?

The bigger base

Using change of base, log⁡4x=log⁡2xlog⁡2y\log_4x = \frac{\log_2x}{\log_2y}. What is yy?

y=4y=4

What is the value of log⁡24\log_24?

22

Solving log⁡2x⋅log⁡4x=92\log_2x \cdot \log_4x=\frac{9}{2} gives which values of xx?

x=8x=8 and x=18x=\frac{1}{8}

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