Question

4^x+2+2^x+3=96.find the value of x.

Answer 1

Answer:

x =

Explanation:

It is given that,

4^x+2+2^x+3=96.

=>4^x *4² + 2^x *2³-96 = 0

=> 16(2^x)²+8(2^x)-96 = 0

Let 2^x = a ----(1)

=> 16a²+8a-96 = 0

On dividing each term by 16 ,we

get

=> a²+a/2-6=0

=> a² + 2*a*(1/4)= 6

=> a²+2*a*(1/4)+(1/4)²=6+(1/4)²

=> (a+1/4)² = 6 + 1/16

=> (a+1/4)² = (96+1)/16

Answer 2

Answer:

Step-by-step explanation:

4^x+2 + 2^x+3 = 96

4^x(4)^2 + 2^x(2)^3 = 96

4^x(16) +2^x(8) = 96

4(2)^x{4(2)^x + 2} = 96

2^x{4(2)^x + 2} = 24

2^x{2[2(2)^x + 1]} = 24

2^x{2(2)^x + 1} = 12

2^x{2 + 1} = 12

2^x = 12/3

2^x = 4

2^x = 2^2

then x = 2

Hence the value x is 2