$7^{2 \log _{7} 5}$ is equal to

Let $n$ be a positive integer such that $\log _2 \log _2 \log _2 \log _2 \log _2(n) < 0 < \log _2 \log _2 \log _2 \log _2(n)$. Let $l$ be the number of digits in the binary expansion of $n$. Then the minimum and the maximum possible values of $l$ are

Number of solution$(s)$ of the equation $\ln(1 + \sin^2 x) = 1 - \ln(5 + x^2)$ is -

If $x+\log _{10}\left(1+2^{x}\right)=x \log _{10} 5+\log _{10} 6$, then the value of $x$ is

The number of solutions of $\log_{4}(x - 1) = \log_{2}(x - 3)$ is:

The sum of all the real solutions of the equation $ \log_{(x+3)}(6x^{2}+28x+30)=5-2\log_{(6x+10)}(x^{2}+6x+9) $ is equal to: