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

Sum

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

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