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

The numbers $2^{2024}$ and $5^{2024}$ are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is

Let $a, b, c$ be real numbers greater than 1, and $n$ be a positive real number not equal to 1. If $log_n(log_2a) = 1; log_n(log_2b) = 2$ and $log_n(log_2c) = 3$ then which of the following is true?

If $4^{\log_2{x}} - 4x + 9^{\log_3{y}} - 16y + 68 = 0$, then $y - x$ equals:

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

Suppose that $\log_2[\log_3 (\log_4a)] = \log_3 [\log_4 (\log_2b)] = \log_4 [\log_2 (\log_3c)] = 0$ then the value of $a + b + c$ is

If $\log_3(x^2 - 1)$, $\log_3(2x^2 + 1)$ and $\log_3(6x^2 + 3)$ are the first three terms of an arithmetic progression, then the sum of the next three terms of the progression is