Question

if 9power x + 2 = 720 +9 power X find the value of (4x)power 1/2

Answer 1

Given expression , $\bold{9^{x+2}=720+9^x}$

$\bold{9^{x+2}=720+9^x}\\\\\bold{9^x.9^2=720+9^x}\\\\\bold{81.9^x=720+9^x}\\\\\bold{80.9^x=720}\\\\\bold{9^x=9}$
∴ x = 1

Now, values of $\bold{(4x)^{1/2}}$ = (4 × 1)^(1/2) = 2

Hence, answer is 2

Answer 2

Hello Dear.

Here is the answer---


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As per as the Question,Conditions will be---

    9 ˣ ⁺ ² = 720 + 9 ˣ

We know,

   Aⁿ ⁺ ¹ = Aⁿ × A¹

Thus, Applying this in the given equation,

         9ˣ × 9² = 720 + 9ˣ
   ⇒   9ˣ × 81 = 720 + 9ˣ
  ⇒  9ˣ  × 81 - 9ˣ = 720
 ⇒ 9ˣ ( 81 - 1) = 720
 ⇒ 9ˣ  × 80 = 720
 ⇒  9ˣ = 720/80
 ⇒ 9ˣ = 9¹

On Comparing,

           x = 1

Thus,

(4x)^1/2 = [4(1)]¹⁾²
              = (4)¹⁾²
              = (2)² ˣ ¹⁾²
              = 2.

Thus, the correct answer is 2.


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Hope it helps.

Have a Marvelous day.