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Solve : (Sqrt(3))^( X - 3 ) = ( Root(4)(3))^( X + 1 ) - Mathematics

Sum

Solve : `(sqrt(3))^( x - 3 ) = ( root(4)(3))^( x + 1 )`

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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

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 4.3 | Page 100
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