Question

If 4^x

+ 4^x–1

= 10 then what is the value of (2x)^

x

?​

Answer 1

Answer:

Step-by-step explanation:

4ˣ + 4ˣ⁻¹ = 10

=> 4ˣ + 4ˣ/4 = 10

//taking 4ˣ common

=> 4ˣ( 1 + 1/4) = 10

=>4ˣ * 5/4 = 10

=> 4ˣ = 10 * 4/5

=> (2²)ˣ = 8

=> 2²ˣ = 2³

//when bases are same, powers are equal

2x = 3

=> x = 3/2

Now,

(2x)ˣ = (2 * 3/2)³/²

         = (3)³/²

         = √27 = 3√3.