Question

Find x, if : `(root(3)( 2/3))^( x - 1 ) = 27/8`

Answer 1

`(root(3)( 2/3))^( x - 1 ) = 27/8`

`[(2/3)^(1/3)]^( x - 1 ) = 3^3/2^3`

⇒ `(2/3)^[( x - 1 )/3] = (3/2)^3`

⇒ `(2/3)^[( x - 1 )/3] = (2/3)^-3`

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

⇒ x - 1 = - 9
⇒ x = - 9 + 1
⇒ x = - 8