IPMAT Indore 2024 (MCQ) PYQs

The product of the roots of the equation $\log_{2} 2^{(\log_{2}x)^{2}} -5 \log_{2}x+6=0$ is

If $\log_{25} [5 \log_3 (1+\log_3(1+2\log_2x))] = \frac12$ then $x$ is:

If $\log _{\left(x^{2}\right)} y+\log _{\left(y^{2}\right)} x=1$ and $y=x^{2}-30$, then the value of $x^{2}+y^{2}$ is ___________.