JAMB Mathematics 2023 Paper

Concept:Use logarithm laws to combine terms and then compare the arguments of equal-base logs.Explanation:Write $3$ as $3\log_2 2$ because $\log_2 2 = 1$.$\log_2(6-x) = 3\log_2 2 - \log_2 x$Apply the power rule: $3\log_2 2 = \log_2 2^3 = \log_2 8$.$\log_2(6-x) = \log_2 8 - \log_2 x$Use the quotient rule: $\log_2 a - \log_2 b = \log_2\left(\frac{a}{b}\right)$.$\log_2(6-x) = \log_2\left(\frac{8}{x}\right)$Since the bases are equal, equate the arguments: $6-x = \frac{8}{x}$.Multiply both sides by $x$: $x(6-x) = 8$This simplifies to $6x - x^2 = 8$, or $x^2 - 6x + 8 = 0$.Factorise: $(x - 4)(x - 2) = 0$So $x = 4$ or $x = 2$.Both values are valid because they satisfy $x > 0$ and $6 - x > 0$.Answer:$x = 4$ or $x = 2$, so the correct option is A.