Question

02^2x+3=65(2^x-1)+57​

Answer 1

2^2x+3 − 65(2x−1) = 57

⇒2^2x . 23 − 65(2x−1) = 57

⇒(2x)2 . 8 − 65(2x−1) = 57

Put 2x = y in the above equation, we get⇒y^2 . 8 − 65(y − 1) = 57

⇒8y^2 − 65y + 65 = 57

⇒8y^2 − 65y + 8 = 0

⇒8y^2 − 64y − y + 8 = 0

⇒8y(y − 8) − 1(y − 8) = 0

⇒(8y − 1)(y − 8) = 0

⇒8y − 1 = 0 or y − 8 = 0

⇒y = 18 or y = 8

⇒2x = 123 or 2x = 23

⇒2x = 2−3 or 2x = 23

⇒x = −3 or x = 3

Answer 2

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