02. Logarithms question bank (Maths)

Given \(\log_3 a = p = \log_b c\) and \(\log_b 9 = \dfrac{2}{p^2}\). If  
\[
\log_9\left(\dfrac{a^4 b^3}{c}\right) = \alpha p^3 + \beta p^2 + \gamma p + \delta \quad (\forall\ p \in \mathbb{R} - \{0\})
\]  
then \((\alpha + \beta + \gamma + \delta)\) equals  

The greatest value of \((4 \log_{10} x - \log_x(0.0001))\) for \(0 < x < 1\) is –