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WAEC Mathematics 2014 Paper

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Question : 32

Total: 49

If log 5.957 = 0.7750, find log

3\sqrt{0.0005957}

4.1986
2.9250
1.5917
1.2853

Solution:

Concept:

Use the power rule of logarithms after writing the number in standard form.

Explanation:

Here,

3\sqrt{0.0005957}

means the cube root, written as

\sqrt[3]{0.0005957}

or

(0.0005957)^{\frac{1}{3}}

.

Given

\log 5.957 = 0.7750

.

Also,

0.0005957 = 5.957 \times 10^{-4}

.

So,

\log(0.0005957) = \log 5.957 + \log 10^{-4}

= 0.7750 - 4 = -3.2250

.

Now,

\log\left((0.0005957)^{\frac{1}{3}}\right) = \frac{1}{3} \log(0.0005957)

= \frac{1}{3} \times (-3.2250) = -1.0750

.

Expressing

-1.0750

as a bar notation logarithm gives

\bar{2}.9250

.

Answer:

\bar{2}.9250

, which is option B.

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