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JAMB Mathematics 2020 Paper

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Question : 11

Total: 40

If log

_{10}

2 = 0.3010 and log

_{10}

3 = 0.4771, eventually without using the logarithm tables, log

_{10}

4.5

0.3010
0.4771
0.6532
0.9542

Solution:

Concept:

Express

4.5

as a quotient of powers of

3

and

2

, then use logarithm laws.

Explanation:

Write

4.5 = \frac{9}{2} = \frac{3^2}{2}

.

So,

\log_{10}4.5 = \log_{10}\left(\frac{3^2}{2}\right)

.

Apply the laws of logarithms:

\log_{10}\left(\frac{a}{b}\right) = \log_{10}a - \log_{10}b

and

\log_{10}(a^n) = n\log_{10}a

.

Therefore,

\log_{10}4.5 = 2\log_{10}3 - \log_{10}2

.

Substitute the given values:

2(0.4771) - 0.3010 = 0.9542 - 0.3010 = 0.6532

.

Answer:

\log_{10}4.5 = 0.6532

, which is option C.

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