# If `4^x-4^(x-1) = 24` , then `(2x)^x` is equal to: (a) 5`sqrt(5)` (b) 25 (c) 125 (d) 25`sqrt(5)` (e) none of these

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Expert Answers

jeew-m | Certified Educator

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

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

`3 xx 4^(x-1)=24`

`4^(x-1)=8`

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

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

By comparing the indices;

`2(x-1)=3`

`x=(5/2)`

`(2x)^x=(2 xx (5/2))^(5/2) `

`= (5)^(5/2) `

`= sqrt [(5)^5] `

`=sqrt (5) xx 5^2 `

`= 25 sqrt(5)`

*So the correct answer is at option (d)*