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Solve : 3^X^2 : 3x = 9 : 1 - Mathematics

Sum

Solve : `[3^x]^2` : 3x = 9 : 1

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Solution

`[3^x]^2` : 3x = 9 : 1

⇒ `[3^x]^2/3^x = 9/1`

⇒ `[3^x]^2 = 9 xx 3^x`

⇒ `[3^x]^2 = 3^2 xx 3^x`

⇒ `[3^x]^2 = 3^(x + 2)`

We know that if bases are equal, the powers are equal.
⇒ x2 = x + 2
⇒ x2 - x - 2 = 0
⇒ x2 - 2x + x - 2 = 0
⇒ x( x - 2 ) + 1( x - 2 ) = 0
⇒ ( x + 1 )( x - 2 ) = 0
⇒ x + 1 = 0            or      x - 2 = 0
⇒ x = - 1                or      x = 2.

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 3.2 | Page 100
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