Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2024Paper 1
Exam
JEE Advanced
Year
2024
Paper
Paper 1
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Advanced 2024 · Paper 1 · Mathematics · Basics of Mathematics

Let a=3 2 and b= 1 5^ 1 / 6 6 . If x, y ∈ ℝ are such that gathered...

Let a=32a=3 \sqrt{2} and b=151/66b=\frac{1}{5^{1 / 6} \sqrt{6}}. If x,y∈Rx, y \in \mathbb{R} are such that 3x+2y=log⁡a(18)542x−y=log⁡b(1080)\begin{gathered}3 x+2 y=\log _a(18)^{\frac{5}{4}} \\2 x-y=\log _b(\sqrt{1080})\end{gathered} and then 4x+5y4 x+5 y is equal to . ________.

Correct answer

0

Step-by-step solution

3x+2y=log⁡32(32)52=52⇒6x+4y=5……(1)\begin{aligned} & 3 x+2 y=\log _{3 \sqrt{2}}(3 \sqrt{2})^{\frac{5}{2}}=\frac{5}{2} \\ & \Rightarrow \quad 6 x+4 y=5 \quad \ldots \ldots(1)\end{aligned}2 x-y=\log _{\frac{1}{5^{1 / 6} \sqrt{6}}}\left(5^{\frac{1}{6}} \sqrt{6}\right)^3=-3 ⇒2x−y=−3.....(2) equation (1) −(2)⇒4x+5y=8\begin{array}{ll}\Rightarrow & 2 x-y=-3 \quad.....(2)\\ & \text{ equation (1) }-(2) \\ \Rightarrow \quad & 4 x+5 y=8\end{array}
Practice Basics of Mathematics on Quantrex Academy →

More from Basics of Mathematics

All Basics of Mathematics questions Full Basics of Mathematics list Basics of Mathematics JEE Maths PYQsJEE Mathematics PYQs All JEE Advanced PYQs