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JAMB Mathematics 2014 Paper

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Question : 8

Total: 47

Evaluate Log₂8 + Log₂16 - Log₂4

3
4
5
6

Solution:

Concept:

Use the logarithm laws to combine the terms into one logarithm.

Explanation:

Given:

\log_2 8 + \log_2 16 - \log_2 4

Use

\log_a x + \log_a y = \log_a (xy)

and

\log_a x - \log_a y = \log_a \left(\frac{x}{y}\right)

.

\log_2 8 + \log_2 16 - \log_2 4 = \log_2 \left(\frac{8 \times 16}{4}\right)

\frac{8 \times 16}{4} = \frac{128}{4} = 32

So,

\log_2 8 + \log_2 16 - \log_2 4 = \log_2 32

Since

32 = 2^5

, we have

\log_2 32 = \log_2 (2^5) = 5\log_2 2 = 5 \times 1 = 5

Answer:

5

(Option C)

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