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Question
Solve : `(sqrt(3))^( x - 3 ) = ( root(4)(3))^( x + 1 )`
Solution
`(sqrt(3))^( x - 3 ) = ( root(4)(3))^( x + 1 )`
⇒ `(3^(1/2))^( x - 3 ) = (3^(1/4))^( x + 1 )`
⇒ `3^[( x - 3)/2] = 3^[( x + 1 )/4]`
⇒ `[ x - 3 ]/2 = [ x + 1 ]/4`
⇒ 4( x - 3 ) = 2( x + 1 )
⇒ 4x - 12 = 2x + 2
⇒ 4x - 2x = 12 + 2
⇒ 2x = 14
⇒ x = `14/2`
⇒ x = 7
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