# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Logarithm Questions | Question 11

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Question 11 : If x is a positive quantity such that 2x = 3log52 , then x is equal to

1. log59
2. 1 + log5$$frac{3}{5}$ 3. 1 + log3$$$frac{5}{3}$) 4. log58 ## ⏰ Last Intake for CAT '21 Crash course! Buy now for just Rs. 8000. Valid until 27th Sep #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2021Online Batches Available Now! ### Explanatory Answer ##### Method of solving this CAT Question from Logarithms Given, 2x = 3log52 Taking log on both sides, we get log$2x) = log (3log52)
x × log(2) = log5(2) × log(3)
x = $$frac{log_5 2 × log 3}{log 2}$ Let us consider the base as 3, x = $\frac{log_52 × log_3 3}{log_3 2}$ x = $\frac{log_5 2 × 1}{log_3 2}$ x = $\frac{1}{𝑙𝑜𝑔_2 5}$ / $\frac{1}{𝑙𝑜𝑔_2 3}$ = $\frac{log⁡_2 3}{𝑙𝑜𝑔_2 5}$ = log5$3)
Going through the options, Simplifying (B)
1 + log5 ($$frac{3}{5}$) 1 + log5$3) - log5(5)
1 + log5(3) – 1
log5(3)

The question is " If x is a positive quantity such that 2x = 3log52 , then x is equal to "

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