If 4-x-x-256- then the value of x is

The correct option is B 4Given, nbsp;(4^√(x))^√(x)=256. We know that 256 = 4^4. ⇒ (4^√(x))^√(x)= 4^4 ⇒ (4)^√(x)×√(x)=4^4 (∵ (a^m)^n=a^mn) ⇒ 4^x=4^4 Sin ...

If 4√x√x=256,...

Question

If $(4^{\sqrt{x}})^{\sqrt{x}} = 256,$ then the value of $x$ is ___.

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\sqrt{2}

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Solution

The correct option is B 4
Given, $(4^{\sqrt{x}})^{\sqrt{x}} = 256.$

We know that $256 = 4^{4} .$

$\Rightarrow (4^{\sqrt{x}})^{\sqrt{x}} = 4^{4}$

$\Rightarrow (4)^{\sqrt{x} \times \sqrt{x}} = 4^{4} (∵ (a^{m})^{n} = a^{m n})$

$\Rightarrow 4^{x} = 4^{4}$

Since bases are equal, their powers must also be equal.
$\Rightarrow x = 4$

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The correct option is B 4Given, (4√x)√x=256. We know that 256=44. ⇒(4√x)√x=44 ⇒(4)√x×√x=44 (∵(am)n=amn) ⇒ 4x=44 Since bases are equal, their powers must also be equal. ⇒x=4

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