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WAEC Further Mathematics 2025 Paper

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Question : 14

Total: 40

Evaluate log

_{0.25}

8

- $\frac{3}{2}$
$\frac{2}{3}$
$\frac{3}{2}$
- $\frac{2}{3}$

Solution:

Concept:

Use the change of base definition: if

\log_a b = y

, then

b = a^y

.

Explanation:

Let

y = \log_{0.25} 8

.

Then

8 = (0.25)^y

.

Write both sides as powers of

2

.

0.25 = \frac{1}{4} = 2^{-2}

, so

(0.25)^y = (2^{-2})^y = 2^{-2y}

.

Also,

8 = 2^3

.

Thus,

2^3 = 2^{-2y}

.

Equating exponents:

3 = -2y

.

Solving gives

y = -\frac{3}{2}

.

Answer:

-\frac{3}{2}

Option A.

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