Simplify: ₁0} 6 - 3 log₁0} 3 + \; 2/3 ₁0} 27

Correct Answer is : log⁡102₁0}²log102

Correct Answer is : log⁡102₁0}²log102

Test Index

WAEC Mathematics 2019 Paper

Question : 14

Total: 50

Simplify:

\log_{10}

_{10}

\; \frac{2}{3} \log_{10} 27

Solution:

Concept:

Use logarithm laws: the power rule, then the product and quotient rules to combine the terms into a single logarithm.

Explanation:

Start with

T = \log_{10}6 - 3\log_{10}3 + \frac{2}{3}\log_{10}27

Apply the power rule:

3\log_{10}3 = \log_{10}(3^3) = \log_{10}27

Also,

\frac{2}{3}\log_{10}27 = \log_{10}(27^{2/3}) = \log_{10}9

T = \log_{10}6 - \log_{10}27 + \log_{10}9

Use

\log A - \log B + \log C = \log\left(\frac{AC}{B}\right)

Therefore,

T = \log_{10}\left(\frac{6 \times 9}{27}\right) = \log_{10}\left(\frac{54}{27}\right) = \log_{10}2

Answer:

\log_{10}2

which is Option B.

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