Question

if 4^x-4^x-1=24 then 2x^2 is equal to what

Answer 1

Answer:

4^x - 4^(x-1) = 24 => 4^(x-1){4–1} = 24

=> 4^(x-1)×3 =24 => 4^(x-1)= 24/3

=>4^(x-1)= 8 => {(2^2)^(x-1)} = 2^3

=> 2^(2x-2) =2^3 ( since {a^m)^n} = a^mn)

=> 2x - 2 = 3 (since a^m=a^n=> m= n)

=> x = 5/2.

So. {(2x)^x}= {(2×5/2)}^(5/2)=5^(5/2) = 5^2×5^(1/2)

= 25√5

Answer 2

${4}^{x} - {4}^{x - 1} = 24$

${2}^{2x} - {2}^{2x - 2} = 24$

${2}^{2x} - {2}^{2x - 2} = 32 - 8$

${2}^{2x} - {2}^{2x - 2} = {2}^{5} - {2}^{3}$

$2x = 5 \: and \: 2x - 2 = 3$

$\therefore x = \frac{5}{2}$

2x² = 2 × (5/2)²

2x² = 2 × 25/4

2x² = 25/4