Let a=3 √(2) and b=frac 1 5 1 / 6 √(6) . If x, y in R are such that 3 x+2 y=log a (18) 5 / 4 and 2 x-y=log b (√(1080)) then 4 x+5 y is equal to

Mathematics · Logrithms

JEE Advanced 2024 — Paper 1 — Question 8

Let $a=3 \sqrt{2}$ and $b=\frac{1}{5^{1 / 6} \sqrt{6}}$ . If $x, y \in R$ are such that $3 x+2 y=\log _{a}(18)^{5 / 4} \text { and } 2 x-y=\log _{b}(\sqrt{1080})$ then $4 x+5 y$ is equal to

Answer: 8

Numerical answer — enter this value.

Step-by-step solution

$\quad a=3 \sqrt{2}, b=\frac{1}{5^{1 / 6} \sqrt{6}}$

$3 x+2 y=\log _{\sqrt{18}} 18^{5 / 4}=\frac{5}{2}$

$2 x-y=-\log _{\left(5^{1 / 6} \sqrt{6}\right)} \sqrt{1080}=-3$

$\Rightarrow 6 x+4 y=5 \rightarrow(1)$

$2 x-y=-3 \rightarrow(2)$

Now, subtract (2) from (1)

$4 x+5 y=8$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2024
Paper: Paper 1
Subject: Mathematics
Chapter: Logrithms
Topic: Fundamentals of Logarithms