Question

If


`\\ \rm\Rrightarrow 4^x-4^(x-1)=24,`

then (2x)^x equals

(a) 5√5

(b) √5

Note:-

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Proper explanation is mandatory .


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​

Answer 1

Explanation:

Let
`4^(x)=y`, then we obtain that:

`4^(x)-4^(x-1)=24\rightarrow y-(y/4)=24 \rightarrow (3y)/(4)=24`

So, we can get:
`3y=96 \rightarrow y = 96/3 = 32`

Now, because
`y=4^(x)=32`, we can obtain the value of x as follows:

`4^(x)=(2^(2))^(x)=(2^(5)) \rightarrow 2x = 5 \rightarrow x=5/2`

Then
`(2x)^(x)=(2(5/2))^(5/2)=5^(5/2)=\sqrt{5^(5)}=25\sqrt 5`

There is no answer in your question.

Answer 2

`\\ \sf\Rrightarrow 4^x-4^(x-1)=24`

`\\ \sf\Rrightarrow 4^x-4^x4^(-1)=24`

`\\ \sf\Rrightarrow 4^x(1-0.25)=24`

`\\ \sf\Rrightarrow 4^x(0.75)=24`

`\\ \sf\Rrightarrow 4^x=32`

`\\ \sf\Rrightarrow 2^(2x)=2^5`

`\\ \sf\Rrightarrow 2x=5`

`\\ \sf\Rrightarrow (2x)^x=(5)^x`