Advertisement Remove all ads

Solve : 8 X 22x + 4 X 2x + 1 = 1 + 2x - Mathematics

Sum

Solve : 8 x 22x + 4 x 2x + 1 = 1 + 2x

Advertisement Remove all ads

Solution

8 x 22x + 4 x 2x + 1 = 1 + 2x

⇒ 8 x `(2^x)^2` + 4 x 2x x 21 = 1 + 2x
⇒ 8 x `(2^x)^2` + 4 x 2x x 21 - 1 - 2x = 0
⇒ 8 x `(2^x)^2` + 2 x ( 8 - 1 ) - 1 = 0
⇒ 8 x `(2^x)^2` + 7( 2) - 1 = 0
⇒ 8y2 + 7y - 1 = 0                   [ y = 2x ]
⇒ 8y2 + 8y - y - 1 = 0
⇒ 8y( y + 1 ) - 1( y + 1 ) = 0
⇒ ( 8y - 1 )( y + 1 ) = 0

⇒ 8y = 1  or  y = - 1

⇒ y = `1/8`  or  y = -1

⇒ 2x = `1/8` or 2x = - 1

⇒ 2x = `1/2^3` or 2x = - 1

⇒ 2x = `2^-3` or 2x = - 1
⇒ x = - 3
[ ∵ 2x  = - 1 is not possible. ]

Concept: Solving Exponential Equations
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 4.1 | Page 100
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×