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WAEC Mathematics 2015 Paper

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Question : 6

Total: 45

Given that logx 64 = 3, evaluate x log

_2

8

6
9
12
24

Solution:

Concept:

Use the definition of logarithms to find the value of

x

, then simplify the logarithmic expression using the power rule.

Explanation:

Given:

\log_x 64 = 3

.

This means

x^3 = 64

.

Since

64 = 4^3

, we can write

x^3 = 4^3

.

Hence,

x = 4

.

Now evaluate

x\log_2 8

:

x\log_2 8 = 4\log_2 8

.

We know

\log_2 8 = \log_2 (2^3) = 3\log_2 2

.

Since

\log_2 2 = 1

, we get

\log_2 8 = 3 \times 1 = 3

.

Therefore,

4\log_2 8 = 4 \times 3 = 12

.

Answer:

x\log_2 8 = 12

(Option C).

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