Find the Value of X in the Following: `(Sqrt(3/5))^(X+1)=125/27` - Mathematics

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Find the value of x in the following:

`(sqrt(3/5))^(x+1)=125/27`

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Solution

Given `(sqrt(3/5))^(x+1)=125/27`

`(sqrt(3/5))^(x+1)=(5/3)^3`

`rArr(3/5)^((x+1)/2)=(3/5)^-3`

On comparing we get,

`(x+1)/2=-3`

⇒ x + 1 = -3 x 2

⇒ x + 1 = -6

⇒ x = -6 - 1

⇒ x = -7

Hence, the value of x = -7.

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Chapter 2: Exponents of Real Numbers - Exercise 2.2 [Page 26]

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RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Exercise 2.2 | Q 10.9 | Page 26

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