Solve: \(13^{\sqrt{x}} = 4^4 – 3^4 – 6\)
Solution
\[ 13^{\sqrt{x}} = 4^4 – 3^4 – 6 \]
\[ \Rightarrow 13^{\sqrt{x}} = 256 – 81 – 6 \]
\[ \Rightarrow 13^{\sqrt{x}} = 169 \]
\[ \Rightarrow 13^{\sqrt{x}} = 13^2 \]
\[ \Rightarrow \sqrt{x} = 2 \]
\[ \Rightarrow x = 4 \]
Final Answer:
\[ \boxed{x = 4} \]