Question

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

Answer 1

Answer: (5^5/2)

Step-by-step explanation:

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

=> 4^(x - 1)(4 - 1) = 24                    [Taking 4^(x - 1) common]

=> 3 * 4^(x - 1) = 24

=> 4^(x - 1) = 8

=> (2^2)^(x - 1) = 2^3

=> 2^(2x - 2) = 2^3

This gives 2x - 2 = 3

=> 2x = 5

=> x = 2.5

So (2x)^x = (2*2.5)^2.5

=> 5^(5/2)