IPMAT Indore 2023 (SA) 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

The value of $(0.04^{log_{\sqrt{5}}(\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + ...)})$ is __________.

The inequality $\log_{a}{f(x)} < \log_{a}{g(x)}$ implies that