Embibe Experts Solutions for Chapter: Logarithm and its Applications, Exercise 2: Exercise-2

If $k=\frac{\log \left(\sqrt{3^{{\log }_{3}25}-{25}^{{\log }_{5}4}}+1\right)}{\log \left(3-\sqrt{3^{{\log }_{3}5}-5^{{\log }_{5}4}}\right)}$, then the value of ${\log }_{k}512$ is

Set of all real values of $x$ satisfying the inequation $\frac{{\log }_2\left(x^2-5x+4\right)}{{\log }_2\left(x^2+1\right)}>1$ is

The solution set of the inequality $\frac{\left(3^x-4^x\right)·\ln \left(x+2\right)}{x^2-3x-4}\le 0$ is

If $\frac{1}{2}\le {\log }_{0.1}x\le 2,$ then

Which of the following is correct?

The domain of the function $f\left(x\right)={\log }_{1/2}\left(-{\log }_2\left(1+\frac{1}{\sqrt[4]{x}}\right)-1\right)$ is

If ${\mathrm{q}}^2-4\mathrm{pr}=0,\mathrm{p}>0,$ then the domain of the function $\mathrm{f}\left(\mathrm{x}\right)=\log \left({\mathrm{px}}^3+(\mathrm{p}+\mathrm{q}){\mathrm{x}}^2+(\mathrm{q}+r)x+r\right)$ is

The range of the function $f\left(x\right)={\log }_{\sqrt{2}}\left(2-{\log }_2\left(16{\sin }^{2}x+1\right)\right)$ is