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Find the Value of X in the Following: `(3/5)^X(5/3)^(2x)=125/27` - CBSE Class 9 - Mathematics

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Question

Find the value of x in the following:

`(3/5)^x(5/3)^(2x)=125/27`

Solution

Given `(3/5)^x(5/3)^(2x)=125/27`

`3^x/5^x xx5^(2x)/3^(2x)=125/27`

`3^x/3^(2x)xx5^(2x)/5^x=125/27`

`5^(2x-x)/3^(2x-x)=125/27`

`5^(2x-x)/3^(2x-x)=5^3/3^3`

`(5/3)^(2x-x)=(5/3)^3`

Comparing exponents we get

2x - x = 3

x = 3

Hence, the value of x = 3.

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 2: Exponents of Real Numbers
Ex. 2.20 | Q: 10.3 | Page no. 26

Video TutorialsVIEW ALL [1]

Solution Find the Value of X in the Following: `(3/5)^X(5/3)^(2x)=125/27` Concept: Laws of Exponents for Real Numbers.
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