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