4. Solve for \( x \) in the following equation. \( 4^{x+3}=4^{9} \)

Since the bases are the same in the equation \( 4^{x+3}=4^{9} \), we can set the exponents equal to each other. This means: \( x + 3 = 9 \) Now, we can solve for \( x \) by subtracting 3 from both sides: \( x = 9 - 3 \) Therefore, \( x = 6 \). So, the solution is \( x = 6 \).