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WAEC Mathematics 2021 Paper

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Question : 4

Total: 49

If log

_{10}

_{10}

3 = n, find log

_{10}

24 in terms of m and n.

3m + n
m + 3n
4mn
3mn

Solution:

Concept:

Use the product rule of logarithms:

\log(ab) = \log a + \log b

.

Explanation:

Write

24

as

8 \times 3

.

So,

\log_{10} 24 = \log_{10}(8 \times 3)

.

Using the product rule,

\log_{10}(8 \times 3) = \log_{10} 8 + \log_{10} 3

.

Now,

8 = 2^3

, hence

\log_{10} 8 = 3\log_{10} 2

.

Given

\log_{10} 2 = m

, we get

3\log_{10} 2 = 3m

.

Given

\log_{10} 3 = n

.

Therefore,

\log_{10} 24 = 3m + n

.

Answer:

\log_{10} 24 = 3m + n

, so the correct option is A.

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