Question

If \(2^{4} \times 4^{2} = 16^{x} \), then find the value of x.

Answer 1

\(2^{4} \times 4^{2} = 16^{x} \) \( \Rightarrow 2^{4} \times (2^{2})^{2} = [(2)^{4}]^{x} \) \( \Rightarrow 2^{4} \times 2^{4} = 2^{4x}\) \( \Rightarrow 2^{4+4}= 2^{4x} \Rightarrow 2^{8} = 2^{4x} \) Comparing, we get 4x = 8 \( \Rightarrow \) x = \( \frac{8}{4} \) = 2 \( \therefore \) x = 2