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Find X, If : (Root(3)( 2/3))^( X - 1 ) = 27/8 - Mathematics

Sum

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

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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

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 2.4 | Page 100
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