JAMB Mathematics 2021 Paper

Concept:A logarithmic equation of the form $\log_{a} x = c$ can be rewritten in exponential form as $x = a^{c}$.This key idea converts the logarithm into a simple power that can be evaluated directly.Explanation:Start with the given equation: $\log_{9} x = 1.5$.Rewrite it using the exponential form: $x = 9^{1.5}$.Convert the decimal exponent $1.5$ into the fraction $\frac{3}{2}$.So we have $x = 9^{\frac{3}{2}}$.Apply the rule for fractional exponents: $9^{\frac{3}{2}} = (\sqrt{9})^{3}$.Since $\sqrt{9} = 3$, substitute to get $x = 3^{3}$.Evaluate the power: $3^{3} = 3 \times 3 \times 3 = 27$.Therefore, the value of $x$ is $27$, which matches option A.Answer:$x = 27$. The correct option is A.