Find \(x\) and \(y\), if \(5^{3x} = 125\) and \(10^y = 0.001\)
Solution
\[ 5^{3x} = 125 \]
\[ \Rightarrow 5^{3x} = 5^3 \]
\[ \Rightarrow 3x = 3 \]
\[ \Rightarrow x = 1 \]
\[ 10^y = 0.001 \]
\[ \Rightarrow 10^y = 10^{-3} \]
\[ \Rightarrow y = -3 \]
Final Answer:
\[ \boxed{x = 1,\; y = -3} \]