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WAEC Mathematics 2025 Paper

Question : 5

Total: 50

Given that log

_2a

_84

, find a.

Solution:

Concept:

Use the definition of a logarithm to rewrite each side in index form and then compare exponents.

Explanation:

Let

\log_8 4 = y

By definition, this means

8^y = 4

Rewrite both sides using base 2:

8^y = (2^3)^y = 2^{3y}

and

4 = 2^2

2^{3y} = 2^2

Since the bases are equal, equate the exponents:

3y = 2

Therefore

y = \frac{2}{3}

Thus

\log_8 4 = \frac{2}{3}

Given

\log_2 a = \log_8 4

, we get

\log_2 a = \frac{2}{3}

Convert this logarithm to index form:

a = 2^{\frac{2}{3}}

Answer:

a = 2^{\frac{2}{3}}

, which is option B.

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