BECE Mathematics 2020 Paper

Concept:Solve the exponential equation by rewriting both sides with the same base and then comparing the exponents.Explanation:The equation is $4^x = 32$.Write both $4$ and $32$ as powers of $2$: $4 = 2^2$ and $32 = 2^5$.Substitute these into the equation: $(2^2)^x = 2^5$.Using the law of indices, $(a^m)^n = a^{mn}$, simplify the left side: $2^{2x} = 2^5$.Since the bases are the same, the exponents must be equal: $2x = 5$.Divide both sides by $2$: $x = \frac{5}{2}$.Answer:$x = \frac{5}{2} = 2\frac{1}{2}$.