IIM-K (BMSAT) 2025 (QA) PYQs

Let $a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_{7} 25 (\log_7 8 - \log_7 4)}$. Then the value of $5^a$ is

If $x, y, z$ are positive real numbers such that $x^{12} = y^{16} = z^{24}$ and the three quantities $3 \log_y x, 4 \log_z y, n \log_x z$ are in arithmetic progression, then the value of $n$ is

The value of $(\log_{3} 30)^{-1} + (\log_{4} 900)^{-1} + (\log_{5} 30)^{-1}$ is