Solve: \(2^{5x+3} = 8^{x+3}\)
Solution
\[ 2^{5x+3} = (2^3)^{x+3} \]
\[ = 2^{5x+3} = 2^{3x+9} \]
\[ \Rightarrow 5x + 3 = 3x + 9 \]
\[ \Rightarrow 2x = 6 \]
\[ \Rightarrow x = 3 \]
Final Answer:
\[ \boxed{x = 3} \]
\[ 2^{5x+3} = (2^3)^{x+3} \]
\[ = 2^{5x+3} = 2^{3x+9} \]
\[ \Rightarrow 5x + 3 = 3x + 9 \]
\[ \Rightarrow 2x = 6 \]
\[ \Rightarrow x = 3 \]
\[ \boxed{x = 3} \]