Simplify \,1/3 log8 + \,1/3 log 64 - 2 log6

Correct Answer is : log 29\,2/992

Correct Answer is : log 29\,2/992

Test Index

WAEC Further Mathematics 2021 Paper

Question : 4

Total: 38

Simplify

\,\frac{1}{3}

\,\frac{1}{3}

log 64 - 2 log6

Solution:

Concept:

Use the logarithm power rule and the product/quotient rules to combine the terms into a single logarithm.

Explanation:

Apply the power rule:

a\log x = \log x^a

\frac{1}{3}\log 8 = \log 8^{1/3} = \log 2

\frac{1}{3}\log 64 = \log 64^{1/3} = \log 4

2\log 6 = \log 6^2 = \log 36

Thus, the expression becomes

\log 2 + \log 4 - \log 36

Using

\log m + \log n = \log(mn)

and

\log m - \log n = \log\frac{m}{n}

\log(2 \times 4) - \log 36 = \log\frac{8}{36} = \log\frac{2}{9}

Answer:

\log\frac{2}{9}

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