JAMB Mathematics 2012 Paper

Concept:Use the definition of a logarithm: $\log_a b = c$ means $b = a^c$.Then isolate $x$ by taking the square root.Explanation:Start with the given equation: $\log_3(x^2) = -8$.Rewrite it in exponential form. The base is $3$, the exponent is $-8$, and the result is $x^2$.So $x^2 = 3^{-8}$.To solve for $x$, take the square root of both sides.Since $\sqrt{x^2} = |x|$, we have $|x| = \sqrt{3^{-8}} = 3^{-4}$.Thus $x = \pm \frac{1}{3^4} = \pm \frac{1}{81}$.The options list only the positive value $\frac{1}{81}$.Therefore, the expected answer is Option D.Answer:$x = \frac{1}{81}$ (Option D). Strictly, $-\frac{1}{81}$ also satisfies the equation, but only the positive value is given among the choices.