WBJEE · Maths · Basic of Mathematics
If \(\log _3 x+\log _3 y=2+\log _3 2\) and \(\log _3(x+y)=2\), then
- A \(x=1, y=8\)
- B \(x=8, y=1\)
- C \(x=3, y=6\)
- D \(x=9, y=3\)
Answer & Solution
Correct Answer
(C) \(x=3, y=6\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}\text {Hints: } & \log _3 \mathrm{x}+\log _3 \mathrm{y}=2+\log _3 2 \\ & \Rightarrow \mathrm{x} \cdot \mathrm{y}=18 \\ & \log (\mathrm{x}+\mathrm{y})=2 \Rightarrow \mathrm{x}+\mathrm{y}=9 \end{aligned}\) we will get \(x=3\) and \(y=6\)
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
- Let \(a=\min \left\{x^{2}+2 x+3: x \in R\right\}\) and \(b=\lim _{\theta \rightarrow 0} \frac{1-\cos \theta}{\theta^{2}} \cdot\) Then \(\sum_{r=0}^{n} a^{r} b^{n-r}\) isWBJEE 2019 Medium
- In \(\Delta A B C\), if \(a^{2} \cos ^{2} A-b^{2}-c^{2}=0,\) thenWBJEE 2015 Medium
- The equation \(8 x^2+12 y^2-4 x+4 y-1=0\) representsWBJEE 2011 Easy
- If \(\mathrm{f}(5)=7\) and \(\mathrm{f}^{\prime}(5)=7\) then \(\underset{x \rightarrow 5}{ } \frac{x f(5)-5 f(x)}{x-5}\) is given byWBJEE 2010 Easy
- Let A be the set of even natural numbers that are < 8 &
B be the set of prime integers that are < 7
The number of relations from A to B areWBJEE 2024 Easy - Let \(f: R \rightarrow R\) be differentiable at \(x=0\). If f(0)=0 and f'(0)=2, then the value of \[
\left.\lim _{x \rightarrow 0} \frac{1}{x} \mid f(x)+f(2 x)+f(3 x)+\ldots+f(2015 x)\right] \text{ is}
\]WBJEE 2015 Medium
More PYQs from WBJEE
- The work function of Cesium is \(2.27 \mathrm{eV}\). The cut-off voltage which stops the emission of electrons from a cesium cathode irradiated with light of \(600 \mathrm{nm}\) wavelength isWBJEE 2016 Medium
- If the focal length of the eye piece of a telescope is doubled, its magnifying power \((\mathrm{m})\) will beWBJEE 2011 Easy
- In a closed circuit there is only a coil of inductance \(L\) and resistance \(100 \Omega\). The coil is situated in a uniform magnetic field. All on a sudden, the magnetic flux linked with the circuit changes by \(5 \mathrm{Weber}\). What amount of charge will flow in the circuit as a result?WBJEE 2022 Easy
- Let \(\Delta=\left|\begin{array}{ccc}\sin \theta \cos \phi & \sin \theta \sin \phi & \cos \theta \\ \cos \theta \cos \phi & \cos \theta \sin \phi & -\sin \theta \\ -\sin \theta \sin \phi & \sin \theta \cos \phi & 0\end{array}\right|\). ThenWBJEE 2022 Hard
- The equation of the circle passing through the point (1,1) and the points of intersection of \(x^{2}+y^{2}-6 x-8=0\) and \(x^{2}+y^{2}-6=0\) isWBJEE 2013 Easy
- Upon treatment with \(I_{2}\) and aqueous \(\mathrm{NaOH}\), which of the following compounds will form iodoform?WBJEE 2012 Easy