Question

Find x, if : `( sqrt(3/5))^( x + 1) = 125/27`

Answer 1

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

⇒ `[(3/5)^(1/2)]^( x + 1 ) = [ 5 xx 5 xx 5 ]/[ 3 xx 3 xx 3]`

⇒ `(3/5)^[( x + 1 )/2] = (5/3)^3`

⇒ `(3/5)^[( x + 1 )/2] = (3/5)^- 3`

We know that if bases are equal, the powers are equal
⇒ `[ x + 1 ]/2 = -3`

⇒ x + 1 = - 6
⇒ x = - 6 - 1
⇒ x = - 7