02. Logarithms question bank (Maths)

If \( a^4 \cdot b^5 = 1 \), then the value of \( \log_a (a^5 b^4) \) equals  

The expression  
\[
\log_p \left( \sqrt[p]{\sqrt[p]{\sqrt[p]{\cdots \sqrt[p]{p}}}} \right), \text{ with } n \text{ radical signs},\ p \geq 2,\ p \in \mathbb{N},\ n \in \mathbb{N}
\]  
when simplified is