If $\log 2=a, \log 3=b, \log 7=c$ and $6^x=7^{x+4}$,then $x$ is equal to:

If $\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)$,then

The number of solutions of the equation $\log _{2}\left(x^{2}+2 x-1\right)=1$ is

Let $a = 3 \sqrt{2}$ and $b = \frac{1}{5^{\frac{1}{6}} \sqrt{6}}$. If $x, y \in \mathbb{R}$ are such that $3x + 2y = \log_a(18)^{\frac{5}{4}}$ and $2x - y = \log_b(\sqrt{1080})$,then $4x + 5y$ is equal to:

If $n = (1999)!$,then $\sum\limits_{x = 1}^{1999} {{\log }_n x}$ is equal to

Let $\phi (x) = x + 2^{\log_x 3} - 3^{\log_x 2}$. Then which of the following is true?