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JAMB Mathematics 2021 Paper

Question : 27

Total: 40

Simplify 2log

\frac{2}{5}

\frac{72}{125}

+ log 9

Solution:

Concept:

Use the laws of logarithms to combine terms into a single logarithm, then simplify to base 10.

Explanation:

Apply the power rule:

2\log \frac{2}{5} = \log \left(\frac{2}{5}\right)^2 = \log \frac{4}{25}

Combine the logs using product and quotient rules:

\log \frac{4}{25} - \log \frac{72}{125} + \log 9 = \log \left(\frac{\frac{4}{25} \times 9}{\frac{72}{125}}\right)

Simplify the fraction:

\log \left(\frac{36}{25} \times \frac{125}{72}\right) = \log \frac{5}{2}

Rewrite

\frac{5}{2}

\frac{10}{4}

\log \frac{5}{2} = \log \frac{10}{4} = \log 10 - \log 4

Since

\log 10 = 1

and

\log 4 = \log 2^2 = 2\log 2

, we get:

1 - 2\log 2

Answer:

1 - 2\log 2

, which is option D.

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