WAEC Further Mathematics 2023 Paper

Concept:Rewrite both sides of the equation using the same base, then compare the exponents.Explanation:Given equation:$$\left(\frac{1}{9}\right)^{2x-1} = \left(\frac{1}{81}\right)^{2-3x}$$Notice that $\frac{1}{81} = \left(\frac{1}{9}\right)^2$.Using this in the equation:$$\left(\frac{1}{9}\right)^{2x-1} = \left(\frac{1}{9}\right)^{2(2-3x)}$$Simplify the exponent on the right-hand side:$$\left(\frac{1}{9}\right)^{2x-1} = \left(\frac{1}{9}\right)^{4-6x}$$Since the bases are equal, equate the exponents:$$2x - 1 = 4 - 6x$$Add $6x$ to both sides and add $1$ to both sides:$$2x + 6x = 4 + 1$$$$8x = 5$$Divide both sides by $8$:$$x = \frac{5}{8}$$Answer:$$x = \frac{5}{8}$$This value is not listed among the given options.