$\underline{QUESTION 1}$
$We have$
$$\begin{align*}C&= A \log_{200} 5 + B \log_{200}2 \\ &= \log_{200} \left(5^A\right) + \log_{200} \left(2^B \right) \\ &= \log_{200} \left(5^A\times 2 ^B\right)\\ \Rightarrow 200^C &=5^A\times 2 ^B , \text{but }200 = 2^3 \times 5^2 \text{ so} \\ \left(2^3...