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# If 4 X − 4 X − 1 = 24 , Then (2x)X Equals - Mathematics

MCQ

If $4x - 4 x^{- 1} = 24,$ then (2x)x equals

#### Options

• $5\sqrt{5}$

• $\sqrt{5}$

• $25\sqrt{5}$

• 125

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#### Solution

We have to find the value of  (2x)^xif  4^x - 4^(x-1) = 24

So,

Taking 4x as common factor we get

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

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

4^x ((1xx4)/(1 xx4)-1/4) = 24

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

4^x xx 3/4 = 24

4^x = 24 xx 4/3

4^x = 32

2^(2x) =2^5

By equating powers of exponents we get

2x = 5

x=5/2

By substituting x=5/2  in (2x)^x we get

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

= (2xx5/2)^(5/2)

=5^(5/2)

=5^(5 xx1/2)

(2x)^x = 2sqrt(5^5)

=2sqrt (5xx5xx5xx5xx5)

= 5xx5  2sqrt5

= 25sqrt5

Is there an error in this question or solution?
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Q 28 | Page 32
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