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WAEC Further Mathematics 2024 Paper

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Question : 8

Total: 40

If log

{}_{2}^{x}

= 2, evaluate log

{}_{x}^{128}

.

7
2
$\;\frac{7}{2}$
$\;\frac{2}{7}$

Solution:

Concept:

Convert a logarithmic equation to exponential form, then express both numbers with the same base to evaluate the new logarithm.

Explanation:

Given

\log_2 x = 2

.

In exponential form,

x = 2^2 = 4

.

Now evaluate

\log_x 128 = \log_4 128

.

Write

4

as

2^2

and

128

as

2^7

.

Therefore,

\log_4 128 = \log_{2^2} 2^7

.

Using

\log_{a^m} b^n = \frac{n}{m} \log_a b

, we get

\frac{7}{2} \log_2 2

.

Since

\log_2 2 = 1

, the value is

\frac{7}{2}

.

Answer:

\frac{7}{2}

(Option C).

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