To solve the equation \( \log_4(32 + x) = 3 \), we can rewrite it in its exponential form. The equation states that \( 32 + x \) is equal to \( 4^3 \).
Calculating \( 4^3 \):
\[ 4^3 = 64 \]
Now, we can set up the equation:
\[ 32 + x = 64 \]
To find \( x \), we subtract 32 from both sides:
\[ x = 64 - 32 \]
Calculating the right side:
\[ x = 32 \]
Thus, the value of \( x \) is \( \boxed{32} \).
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