Question

Find the value of x in the following:

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

Answer 1

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.