Question

The domain of definition of the function, $f\left(x\right)={\log }_{3/2}{\log }_{1/2}{\log }_{\pi }{\log }_{\pi /4}x$ is

• A. $(0,\infty )$
• B. $(0,{\left(\frac{\pi }{4}\right)}^{\pi })$
• C. $({\left(\frac{\pi }{4}\right)}^{\pi },\frac{\pi }{4})$
• D. $({\left(\frac{\pi }{4}\right)}^{\pi },\infty )$

Answer 1

The correct option is D $({\left(\frac{\pi }{4}\right)}^{\pi },\infty )$

$f\left(x\right)=\frac{\log x}{\log \frac{\pi }{4}}\times \frac{\log \pi }{\log \frac{1}{2}}\times \log \frac{3}{2}$

Clearly the domain of $f\left(x\right)$ is same as that of $\log x$

Hence $x\in (0,\infty )$