WAEC Further Mathematics 2018 Paper

Concept:Use logarithm laws: the power rule and the fact that $2 = \log_{3}9$.Explanation:Start with the equation:$\log_{3}a - 2 = 3\log_{3}b$Rewrite 2 as a logarithm in base 3:$2 = 2\log_{3}3 = \log_{3}3^{2} = \log_{3}9$Also apply the power rule on the right side:$3\log_{3}b = \log_{3}b^{3}$Substitute both into the original equation:$\log_{3}a - \log_{3}9 = \log_{3}b^{3}$Use the quotient law for logarithms:$\log_{3}\left(\frac{a}{9}\right) = \log_{3}b^{3}$Since both sides have the same base, equate the arguments:$\frac{a}{9} = b^{3}$Multiply both sides by 9:$a = 9b^{3}$Answer:$a = 9b^{3}$, which is option C.