Question

If 4^x- 4^x-1=24 then(2x)^x

Answer 1

$\bold{Answer :}$

Now,

4ˣ - 4ˣ⁻¹ = 24

or, 4ˣ (1 - 4⁻¹) = 24

or, 4ˣ (1 - 1/4) = 24

or, 4ˣ {(4 - 1)/4} = 24

or, 4ˣ (3/4) = 24

or, 4ˣ = 24 × (4/3)

or, 4ˣ = 32

or, 2²ˣ = 2⁵

So, 2x = 5

or, x = 5/2

Now, (2x)ˣ

= (2 × 5/2)^(5/2)

= 5^(5/2)

= 5^(2 + 1/2)

= 5² × 5^(1/2)

= 25√5

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