Question

if 4^x-4^(x-1)=24 ,then find the value of (2x)^x .

Answer 1

Heya

4^x-4^(x-1) = 24

4^x - (4^x/4¹) = 24

(4×4^x - 4^x)/4 = 24

3×4^x/4 = 24

4^x = 24×4/3

4^x = 32

2^2x = 2^5

Equating the powers,

2x = 5

x = 5/2

(2x)^x = (2×5/2)^5/2

= 5^(5/2)

= 5^5/5²

= 5³ = 125.

Hope it helps! ^_^