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Solve : 22x + 2x+2 - 4 X 23 = 0 - Mathematics

Sum

Solve : 22x + 2x+2 - 4 x 23 = 0

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Solution

22x + 2x+2 - 4 x 23 = 0
⇒ ( 2x)2 + 2x. 22 - 4 x 2 x 2 x 2 = 0
⇒ ( 2x)2 + 2x. 22 - 32  = 0
Putting y = 2x
⇒ y2 + 4y - 32 = 0
⇒ y2 + 8y - 4y - 32 = 0
⇒ y( y + 8 ) - 4( y + 8 ) = 0
⇒ ( y + 8 )( y - 4 ) = 0
⇒ y + 8 = 0  or  y - 4 = 0
⇒ y = - 8 or y = 4
⇒ 2x = - 8 or 2x = 4
⇒ 2x = 22
[ ∵ 2x = - 8 is not possible. ]
⇒ 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 4.2 | Page 100
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