IPMAT Indore (MCQ) PYQs

If $y=a+b \log _{e} x$ then which of the following is true?

Suppose that a, b, and c are real numbers greater than 1. Then the value of $\dfrac{1}{1+\log_{a^2 b} \frac{c}{a}} + \dfrac{1}{1+\log_{b^2 c} \frac{a}{b}} + \dfrac{1}{1+\log_{c^2 a} \frac{b}{c}}$ is

If $\log_4 x = a$ and $\log_{25} x = b$, then $\log_x 10$ is