If ₃a - 2 = 3₃b, express a in terms of b.

Correct Answer is : a=9b3a = 9b³a=9b3

Correct Answer is : a=9b3a = 9b³a=9b3

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WAEC Further Mathematics 2018 Paper

Question : 8

Total: 40

\log_{3}a - 2 = 3\log_{3}b

, express a in terms of b.

Solution:

$\log_{3}a - 2 = 3\log_{3}b$

Using the laws of logarithm, we know that $2 = 2\log_{3}3 = \log_{3}3^{2}$

$\therefore \log_{3}a - \log_{3}3^{2} = \log_{3}b^{3}$

= $\log_{3}\left(\frac{a}{3^{2}}\right) = \log_{3}b^{3} \implies \frac{a}{9} = b^{3}$

$\implies a = 9b^{3}$

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