AP EAMCET · Maths · Functions
The domain of the real valued function \(f(x)=\log _2 \log _3 \log _5\left(x^2-5 x+11\right)\) is
- A \((2, \infty)\)
- B \((-\infty, 3)\)
- C \((2,3)\)
- D \((-\infty, 2) \cup(3, \infty)\)
Answer & Solution
Correct Answer
(D) \((-\infty, 2) \cup(3, \infty)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \log _3 \log _5\left(x^2-5 x+11\right)\gt0 \\ & \Rightarrow \log _5\left(x^2-5 x+11\right)\gt1 \Rightarrow(x-3)(x-2)\gt0 \\ & \Rightarrow x \in(-\infty, 2) \cup(3, \infty)\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(\int \frac{5 \tan \mathrm{x}}{\tan \mathrm{x}-2} \mathrm{dx}=\mathrm{ax}+\mathrm{b} \log |\sin \mathrm{x}-2 \cos \mathrm{x}|+\mathrm{c}\), then \(\mathrm{a}+\mathrm{b}=\)AP EAMCET 2025 Medium
- The approximate value of \((1.0002)^{3000}\) isAP EAMCET 2002 Medium
- Angle made by the position vector of the point with the positive direction of axis isAP EAMCET 2021 Easy
- If \(\alpha, \beta, \gamma\) are the roots of \(x^3-6 x^2+11 x-6=0\), then the equation having the roots \(\alpha^2+\beta^2, \beta^2+\gamma^2\) and \(\gamma^2+\alpha^2\) isAP EAMCET 2019 Easy
- \(\lim _{x \rightarrow 2} \frac{\sqrt{1+4 x}-\sqrt{3+3 x}}{x^3-8}=\)AP EAMCET 2024 Easy
- \(\lim _{\rightarrow-}\left(\frac{-\pi}{\cos }\right)\) is equal toAP EAMCET 2015 Easy
More PYQs from AP EAMCET
- The equation of lines passing through \((5,3)\) and perpendicular to \(2 x+y-7=0\) isAP EAMCET 2020 Easy
- The area bounded by \(y-1=-|x|\) and \(y+1=|x|\) isAP EAMCET 2023 Easy
- If \(x\)-coordinate of a point \(P\) on the line joining the points \(Q(2,2,1)\) and \(R(5,1,-2)\) is 4 , then the \(z\)-coordinate of \(P\) isAP EAMCET 2012 Easy
- Two closed pipes have the same fundamental frequency. One is filled with oxygen and the other with hydrogen at the same temperature. Ratio of their lengths respectively isAP EAMCET 2015 Easy
- \(\int \frac{x+1}{x\left(1+x e^x\right)} d x\) is equal toAP EAMCET 2015 Medium
- If \(\tan (\pi \cos \theta)=\cot (\pi \sin \theta)\), then a value of \(\cos \left(\theta-\frac{\pi}{4}\right)\) among the following isAP EAMCET 2013 Medium